Selecting from 2 options where it can be either or both

Radio Buttons with 3 Options

In this situation you can easily select a default value, but radio buttons are not the most common thing in mobile. You commonly find single selection lists instead. A different solution is likely the better course.

Dropdown

You simply require an extra click to perform the above option, and you hide the other two possibilities until opened. Many HIGs suggest radio buttons for 1-5 options. From Apple's HIG:

Consider using a pop-up menu if you need to display more than five items. It’s best when a group of radio buttons contains at least two items and a maximum of about five.

Checkboxes with 2 Options

You can easily accomplish this but checkboxes. Assuming there is a "next" button of some sort, the button is simply disabled until one item is checked.

An issue with this process is that the user must realize how to get the "next" button enabled. A small block of text ("select a starter and/or main") can help the user figure this out.

Would you like to... ?

While this may not fit your ultimate use case, your example would fit.

You can provide a "order a starter" button, which takes you through the order process for starters. You can provide a "order a main" button, which takes you through the order process for mains. Feedback on the main screen (holding these buttons) informs the user what they have previously done.

A 3rd button to "finish order" is disabled until at least one of the above processes as been complete.

I would do a simple 3 choice radio button. Here's an example of one I did in 2 minutes with jQuery UI:

 Click to see demo in action

The easiest and most intuitive thing for the first time user is two checkboxes with validation to prevent turning off both. The reasoning is that the user reads down the options one by one and judges each one separately in order. They are not trying to optimize their number of clicks on first visit, they're trying to optimize their cognitive load; as they read down and reach the third option of 'both starter and entree' they have to rethink the options they did before. It is better than three radiobuttons because you have to read three distinct things rather than two, and they'll essentially have to go through all inclusive or thought when they read the third item. It's fun for us to think about but for lay people, they don't want to be bothered with that cognitive overload dealing with the odd 'A and B'.

Validation (restricting and telling the user they must choose at least one) is more code to write, but would have to be done in the radiobutton or dropdown situation, too, or else it will be implicit and invisible to the user which will be confusing to the user (they won't understand why they can't choose nothing).

This UI generalizes easily to any kind of number restriction ('you must choose at least 3 out of 7 items'), whereas radiobuttons have a combinatorial explosion.

For an experienced user (unlikely for a menu), the single click might be a nice efficiency in some contexts, but for a menu one presumably may have different choices every time.

With radiobuttons it requires exactly one action to select (or correct) any of the options.

With checkboxes it takes two to select both and two to change A to B.

I might look at something else if desserts came into the picture, though.