Woot! I am legal. 
In the end, it took about 1 minute at home filling out the form, 5 minutes at Village Hall, giving it to Business Services and then paying the cashier my $25, plus travel time there and back. 30 minutes max. Thanks to the various folks at Village Hall who talked me through my confusion — I hadn’t found the Home Kitchen form initially, and was trying to fill out the Cottage Food form, which is more complicated and requires you to take an 8 hour food safety certification course and pass a test.
The Home Kitchen (aka ‘cupcake law’) is a relatively new ordinance that lets people in Illinois (if their local municipalities adopt it, which Oak Park did about a year ago) sell a small amount of food cooked in their kitchen directly to the public — spices, spice blends, jams and jellies, baked goods, that kind of thing. I’m allowed to do up to $1000 / month, selling directly to the public (no wholesale businesses). If I wanted to do the Cottage Food form (and certification course) as well, I could then sell an additional much larger amount at Farmer’s Markets, but I have no plans to do that. Although I suppose if Kavya & Anand want to pick up some money as a teen, it’d be an interesting option to think about…
Now off to make up an order form for Sri Lankan curry powder…