Pre-cook the potatoes by microwaving them for 5 minutes. Proceed with chopping the potatoes along with the rest of the vegetables. (See notes)
Melt butter in a large skillet, and cook all chopped vegetables EXCEPT tomatoes over medium high heat for 5- 8 minutes. Stir occasionally. If needed, add a little water to the skillet and cover vegetables with a lid to prevent burning.
Meanwhile, beat the eggs and milk together in a separate bowl.
Push the cooked vegetables to the side of the skillet, forming a hole in the center of the pan. Add eggs into the center of the pan and mix until eggs are fully cooked, about 5 minutes.
Top with tomatoes, salt and pepper, and shredded cheese. Cover with a lid until the cheese melts.