Grease a 13x9-in. baking dish and preheat oven to 375F.
Mix together mayonnaise and dijon mustard. Split English Muffins in half. Spread mayo/dijon mixture onto the muffins + place them in the greased baking dish. Top with crab, Old Bay, and lemon juice.
In a large bowl, whisk together eggs, monterey jack, parmesan, gruyere, yellow pepper, red pepper, half-and-half, black pepper, minced onion, red pepper flakes, and kosher salt. Whisk until well-combined. If too thick, add half-and-half a little at a time.
Pour egg and cheese mixture over the English Muffins + crab and spread evenly. Top with extra monterey jack.
Bake for 35-40 minutes, or until a toothpick comes out clean from the center of the casserole. Let it rest for 5-10 minutes. Garnish with parsley.