Preheat oven to 400 degrees. Spray a muffin tin well with non-stick spray.
While the oven is preheating, prepare your vegetables and whisk the eggs with the 1/4 cup of milk.
Place enough of the hashbrown potatoes in the bottom of each muffin tin to cover the bottom. Bake for 10 minutes. Remove from oven and using the bottom of a glass press the hashbrowns down flattening them.
Place back into oven and bake for another 10 minutes, they will start to crisp up. Watch them so they don't burn though.
Remove from oven, reduce oven temperature to 350 degrees.
Top each muffin tin with your choice of vegetables. Pour the egg mixture in each muffin tin, filling them to nearly the top.
Sprinkle cheese on top of each muffin tin.
Bake at 350 degrees for 20 minutes or until the egg is cooked through. Remove from oven. To remove each mini omelet, run a butterknife along the sides of each. Then use an offset spatula or fork to lift each out. I found the offset spatula works great if some of the hashbrowns stick a bit.
Serve warm. If you are freezing any leftovers, cool completely and store in a resealable bag in the freezer.