Step 1: Preheat your broiler to high. Place poblano peppers on a baking sheet. Broil for 5-7 minutes per side, turning occasionally, until skins are charred and blistered. Alternatively, roast over an open flame on a gas burner or grill.
Step 2: Transfer the charred peppers to a bowl and cover tightly with plastic wrap. Let them steam for 10-15 minutes. This makes the skins easy to peel.
Step 3: Once cooled, peel the skins off the peppers, remove the stems, and carefully slice them open to remove the seeds and membranes. Cut the peppers into strips about 1-inch wide.
Step 4: Preheat your oven to 375°F (190°C). Lightly grease a 9x13-inch baking dish with cooking spray or butter.
Step 5: In a large bowl, whisk together the eggs, milk, salt, black pepper, garlic powder, and cumin until well combined.
Step 6: Arrange half of the roasted poblano strips evenly in the bottom of the prepared baking dish.
Step 7: Sprinkle half of the Monterey Jack cheese and half of the cheddar cheese over the poblano layer.
Step 8: Carefully pour half of the egg mixture over the cheese and peppers.
Step 9: Repeat the layers: place the remaining poblano strips, followed by the remaining Monterey Jack and cheddar cheese.
Step 10: Pour the rest of the egg mixture over the top. Evenly distribute the drained diced tomatoes with green chilies over the top layer.
Step 11: Bake for 30-35 minutes, or until the casserole is golden brown, puffed, and the center is set (a knife inserted into the center comes out clean).
Step 12: Remove from the oven and let the casserole rest for 5-10 minutes before serving. This allows the layers to set and makes for easier slicing.