Preheat the oven to 375°F (190°C). Lightly grease an 8-inch (20 cm) shallow baking dish or an ovenproof skillet (about 1 to 1.5 quart) with butter or nonstick spray.

Make Crabmeat Mixture

Soften and Whisk

In a medium mixing bowl, use a rubber spatula or electric hand mixer on low to combine the softened cream cheese until smooth. Add mayonnaise and sour cream and continue to mix until homogenous and slightly airy (about 30–45 seconds).

Flavor Base

Stir in the Dijon mustard, Worcestershire sauce, lemon juice, Old Bay seasoning, smoked paprika, kosher salt, and black pepper until evenly distributed.

Add Cheeses and Herbs

Fold in the grated Parmesan, 1 cup shredded Gruyère (or cheddar), and the chopped chives until combined. Taste and adjust seasoning (add up to 1/4 tsp more salt or a squeeze more lemon if needed).

Fold in Crab

Gently fold the lump crabmeat into the mixture with a spatula, taking care not to break up lumps too much. Ensure crab is evenly distributed but remain delicate to keep nice pieces.

Assemble and Top

Transfer the crab mixture to the prepared baking dish and smooth the top with an offset spatula or the back of a spoon.

Sprinkle the remaining 1/2 cup shredded cheese evenly over the top of the dip. Scatter the buttered breadcrumbs (panko mixed with melted butter) across the surface to create a crunchy gratin topping.

Bake

Place the dish on the middle rack and bake for 18–22 minutes, until the dip is hot and bubbling and the topping is golden brown. If you want a deeper golden crust, broil on high for 1–2 minutes while watching closely to avoid burning.

Finish and Serve

Remove the dip from the oven and let rest for 3–5 minutes. Sprinkle chopped parsley and remaining 1 tablespoon chopped chives over the top. Serve warm with crostinis and lemon wedges on the side.

If desired, toast crostinis just before serving: arrange slices on a baking sheet, brush lightly with olive oil, and bake at 375°F (190°C) for 6–8 minutes until crisp.