01 - Preheat oven to 400°F. Lightly butter a medium gratin or casserole dish and set aside.
02 - In a medium saucepan over medium heat, melt the butter. Whisk in the flour and cook for 1 minute, stirring constantly, until a smooth roux forms.
03 - Gradually whisk in the milk and heavy cream, stirring continually until the sauce is smooth and slightly thickened, about 3 to 4 minutes.
04 - Stir in the Dijon mustard, Worcestershire sauce, cayenne pepper, paprika, sea salt, and black pepper until evenly incorporated.
05 - Remove the saucepan from heat. Stir in half of the cheddar, half of the Gruyère, and all of the Parmesan cheese until fully melted and smooth.
06 - Gently fold the jumbo lump crab meat into the cheese sauce, taking care not to break apart the lumps.
07 - Spoon the crab mixture evenly into the prepared baking dish. Sprinkle the remaining cheddar and Gruyère cheese over the top.
08 - Bake for 20 to 25 minutes until the gratin is bubbling and the top is golden brown.
09 - Allow the gratin to cool slightly. Garnish with chopped fresh parsley and serve with lemon wedges alongside.