Preheat the oven to 425 degrees.
In a bowl, mix the brown rice, egg, and cheese and pour into an 8-by-8-inch baking pan. Transfer to the oven and bake for 10 minutes.
Reduce the temperature to 375 degrees. In a bowl, mix together the remaining ingredients, pour onto the rice crust, and bake until the eggs are set, about 30-35 minutes. Remove from the oven and let cool for 10 minutes before slicing.