What exactly does this refer to? When I think миска, I think of a large round container used when baking: http://goo.gl/DYLNQ8. I believe a bowl that you eat cereal or soup (http://goo.gl/GxNuXR, https://goo.gl/lwvgN2) from is called глубая тарелка ‘deep plate’, or at least that is what my mother calls it. Please, can anyone verify? I don’t know where to look for a good definition of миска.
You can use a dictionary if you wish—the only problem is that definitions of many everyday items want someone to finally update them. «Ми́ска», «пиа́ла» (from Persian peiaale) and sometimes «пло́шка» all refer to a bowl, though it is миска that you'll see in the shop.
In some places, especially in Siberia and the Russian Far East, чашка is used as the name for a bowl. Well, it is a good place to remember that we teach Moscow/St.Petersburg Russian when it matters :).
You should have used ка́ши 'of kasha', not ка́шей 'with kasha'.
The sentence «Я ем ми́ску ка́шей» 'I'm eating a bowl with/using kasha' is completely grammatical, but probably not very useful. Theoretically, you could have freezed your kasha so that it's iced, and made yourself a spoon out of iced-kasha; and миска can be made of something edible, e.g. out of chocolate, so technically this sentence is not completely impossible... :D