01 - Preheat oven to 400°F. 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, to form a smooth roux.
03 - Gradually whisk in the whole milk and heavy cream, stirring until 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 well combined.
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, being careful not to break apart the lumps.
07 - Spoon the crab mixture into the prepared baking dish and sprinkle evenly with the remaining cheddar and Gruyère cheeses.
08 - Bake for 20 to 25 minutes, or until the gratin is bubbling and the top is golden brown.
09 - Let cool slightly, garnish with chopped fresh parsley, and serve with lemon wedges on the side.