Step 1

Arrange a rack in the middle of the oven and heat to 375°F. Coat a 9x13-inch baking dish with olive oil; set aside.

Step 2

Heat the 1 tablespoon of oil in a large frying pan over medium-high heat until shimmering. Add the mushrooms and carrots and cook, stirring occasionally, until tender, about 5 minutes. Add the spinach and toss until wilted and almost all of the liquid is evaporated, about 5 minutes. Remove from the heat and stir in the potatoes and red peppers.

Step 3

Transfer to the baking dish and spread into an even layer. Sprinkle evenly with the cheese. Whisk the eggs, milk, salt, and pepper together in a large bowl. Pour over the vegetables.

Step 4

Bake until the top is slightly golden-brown and a knife inserted in the middle comes out clean, 50 to 55 minutes. Let cool for 5 minutes before slicing and serving.