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 continuously 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. Fold in half of the shredded cheddar, half of the shredded Gruyère, and all of the grated Parmesan, stirring 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 - Transfer the mixture into the prepared baking dish, spreading evenly. Scatter the remaining cheddar and Gruyère across the top.
08 - Bake for 20 to 25 minutes until the gratin is bubbling vigorously and the cheese crust is a rich golden brown.
09 - Allow the gratin to rest for a few minutes. Garnish with chopped fresh parsley and serve alongside lemon wedges.