Preheat the oven to 375°F. Grease a 9 x 9-inch pan that's at least 2 inches deep, or a shallow 2-quart casserole dish.
In a medium skillet over medium heat, melt the butter and pour in the oil. Add the onions and cook until translucent, stirring occasionally. Add the peppers and cook for 1 more minute. Remove from the heat and cool to room temperature.
In a large bowl, combine the cornmeal and milk. Stir in the sugar, cottage cheese, eggs, salt, pepper, and baking powder. Stir in the corn kernels and cooled onion mixture. Stir in the cheese, and then transfer the batter to the prepared pan.
Bake for 40 to 45 minutes, until the center doesn't wobble when lightly touched with your finger. Remove from the oven, serve warm.