Preheat the oven or toaster oven to 450 degrees F (230 degrees C). Lightly grease a baking sheet.

Lightly coat poblano pepper with olive oil; place pepper, opened like a butterfly cut-side up, onto the prepared baking sheet.

Bake in the preheated oven until pepper is tender and skin starts to brown, 20 to 30 minutes. Set aside.

Whisk together eggs and milk in a large bowl; fold in tomato, mushroom, green onion, cilantro, salt, and black pepper.

Melt butter in a skillet over medium heat; cook and gently stir egg mixture in melted butter until eggs are set, about 5 minutes. Spoon egg mixture into poblano pepper and top with Cheddar-Monterey Jack cheese.

Bake until cheese is melted, 3 to 5 minutes.