There are two things you have to realize when baking or cooking in small objects like mugs.
1. They cook FAST.
The container is deeper than it is wide. A baking pan, as a cake pan, is shallow, but wider...giving the cake plenty of open space on top to let air and moisture escape while being baked.
A container like a mug, is deeper and has less of an open top surface for the cake/cookie to bake correctly.
If the item baked is baked too hot, too fast, then it can turn out gooey on bottom and hard on top and not baked well.
If the item baked is baked too low, too slowly, then it can turn to "rubber" or dry out and turn hard.
The trick to baking in something like a mug, is to be sure it is something you CAN bake in. And if you do bake in a mug, bake it in a flat cake pan filled half way with water. The idea of the water is to keep the oven air moisturized so the top of what is being baked in the mug doesn't dry out or crack too badly before the bottom of whats in the mug can get baked.
Bake it on less heat than a regular cake, and bake it for a bit longer.
This takes some experimenting with, as different kinds/types/shapes of mugs and whats being baked in them will all turn out differently.
2. The container (mug) holds the heat in for a longer period of time.
Mugs are usually made of some type of clay or porcelain materials. These hold heat in a lot longer than the metal cake pan you are used to.
In order to keep whatever is being baked from over baking, you need to take it out of the oven 5-10 minutes before it is done, as the heat from the mug itself will keep baking whats inside of it for several minutes.
I would suggest making mini cakes in the microwave instead. Using small baking dishes instead of mugs.
These dishes work better than mugs, for me anyway. But again, because of the kind of container they are, you have to adjust baking times and heat accordingly.
Most of these dishes are about 4-6 inches across and about 1-2 inches deep--
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