Preheat your oven to 350°F / 175°C. Generously grease a baking dish large enough to hold the peppers in a single layer.
Carefully make a slit down the side of each roasted poblano pepper and stuff it with the grated Monterey Jack cheese.
Arrange the stuffed peppers snugly in the prepared baking dish.
In a medium bowl, crack the eggs and add the milk, cumin, salt, and pepper.
Whisk vigorously until the mixture is smooth and slightly frothy.
Gently pour the egg batter evenly over the stuffed peppers in the dish.
Bake uncovered for 25-30 minutes, or until the egg mixture is set, puffed up, and lightly golden on top.
Let it rest for a few minutes before serving.