Crack eggs into a bowl and beat with milk until combined. Melt ½ tablespoon butter in a medium heat skillet. Add egg mixture to skillet. As eggs begin to set, gently pull the eggs across the pan with a spatula. Continue cooking until thickened and no liquid is visible. Remove from heat and keep warm. Melt 1 tablespoon butter in skillet. Add mushrooms, garlic, and Italian seasoning, and cook until tender, about 5–6 minutes. Toast English muffins and top with eggs. Pile mushroom mixture on top of eggs and sprinkle with chives.
Serve with roasted potatoes and broiled tomato.