Lay out the roasted poblano peppers at the base of the casserole dish, ensuring they are spread out evenly without overlap.
Distribute approximately one-third of the shredded Monterey Jack cheese over the layer of peppers.
Add another layer of poblano peppers atop the cheese, then proceed to sprinkle another one-third of the cheese.
Pour the previously prepared egg mixture over the layers in the casserole dish, ensuring even coverage.
Garnish the top with the remaining Monterey Jack cheese.
Position the casserole dish in the preheated oven and bake for a duration of 35-40 minutes, or until the top appears golden brown and the mixture has set.
Upon removal from the oven, let the casserole stand at room temperature for a period of 10 minutes to allow it to set further.
Before serving, if desired, garnish with finely chopped cilantro or parsley.