Preheat oven to 350 degrees Heat the oil in a 10”-12” ovenproof omelet pan. Brown the ground beef, mushrooms and onion. Remove from pan with a slotted spoon and set aside onto a plate. Place the potatoes in the pan and cook over medium-low heat for 8-10 minutes, until tender and brown, tossing occasionally. Remove from pan to the same plate as the ground beef. In a medium bowl, beat the eggs, milk and seasonings together. Using the same omelet pan, wipe out any oil, melt the butter, lower the heat to low and pour in the egg mixture. Add the reserved ingredients over the eggs and place the pan in the oven for about 8-9 minutes, or just until the eggs are set. Slide onto a plate to serve.