You're not missing something simple. This is just a more complicated chart to interpret. The good news is, I've got both a short and a long answer for you.
The Short Answer
Shortly after contacting departure, they will give you a higher altitude to climb to and they will start vectoring you to STOIC. The altitudes listed next to each leg are minimums. They are used for planning purposes or in the event of radio failure. During a normal operations, you will be flying the altitude assigned by ATC.
The Long Answer
There are actually a number of "gotchas" on this chart:
Getting to STOICThere are two types of RNAV departure procedures, Type A and Type B. Type A departures start with a waypoint about 15 NM away from the airport. ATC is usually responsible for giving you vectors to get there. Type B departures have waypoints near the departure end of the runway. These usually have you flying by your own navigation as soon as you takeoff. There is usually a separate transition for each usable runway. The STOIC2 departure is Type A.
Since the STOIC2 is a Type A departure, you would expect the STOIC waypoint to be about 15 NM away from the airport... and you would be correct. So why does it look like it is right on top of the airport? The answer to that question is hiding the lower right corner of the diagram, "NOTE: Chart not to scale." It is fairly common for departures and arrivals to not be drawn to scale, due to the large distances that they cover.
Maintain 3000The next item of note is the initial altitude restriction: "Maintain 3000, expect clearance to filed altitude/flight level 10 minutes after departure." This is slightly confusing, as one of the first things departure will do when you contact them after takeoff is give you a new, higher altitude to maintain. The reason such a low altitude is published on the chart is to keep you from climbing into other traffic before getting in contact with the departure controller. If you are having radio problems and cannot get into contact with ATC, you can climb to the initial cruise altitude that you were cleared for 10 minutes after your departure time.
So, to recap the STOIC2 so far: After takeoff, you are flying the heading assigned by ATC and climbing to 3,000ft. Shortly after contacting the departure controller, they give you a higher altitude to climb to and start vectoring you towards the STOIC waypoint.
Minimum AltitudesNow, as for those altitudes listed next to each leg. The first one is the Minimum En-Route Altitude (MEA). The second one, with the *, is the Minimum Obstruction Clearance Altitude (MOCA). The FAA defines those as follows:
MEA - The MEA is the lowest published altitude between radio fixes that assures acceptable navigational signal coverage and meets obstacle clearance requirements between those fixes.
MOCA - The MOCA is the lowest published altitude in effect between radio fixes... that meets obstacle clearance requirements for the entire route segment. This altitude also assures acceptable navigational signal coverage only within 22 NM of a VOR.
This is where thing start to get fuzzy. The MEAs for some of the legs of departure and arrival procedures are much higher than just what meets the above definition. The MEAs are instead designed to gradually climb you into or descend you out of the en route system. I did a bit of searching, but I could not turn up any solid information on exactly how MEAs are selected for departures or arrivals.
Since this is an RNAV departure, there are no VORs, so you can assume that the MOCA is providing obstacle clearance only.
Using the Minimum AltitudesThere are two ways in which the minimum altitudes are used. First off is planning. If you are going to be taking the WOOLY transition, I would not file an en route altitude any lower than 9,000ft, since it is the highest MEA on the departure.
The second way to use the minimum altitudes is in the event of a two-way radio communication failure in instrument conditions. If you lost the radio after takeoff and could not get in contact with departure, you should climb to the MEA for each leg as you fly the departure. You should do this until 10 minutes after the departure time, at which point you should climb to the cruise altitude you were cleared for.
I could not find a good reference as to why the MOCAs are listed. But I would guess that they are there so that you know how low you can safely fly the leg in an emergency condition, such as icing at higher levels.
When flying the departure normally, you will be climbing to the altitudes assigned by ATC. These will usually meet or exceed the listed MEA.
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You ended up picking a pretty interesting chart to ask about. RNAV procedures are still going though growing pains and the FAA regulations and handbooks have not quite caught up yet. That makes for a lot of mixed or dual use symbology with the older VOR system.