Pick through the jumbo lump crab meat to remove any shells or cartilage. Gently pat dry with paper towels to remove excess moisture, being careful not to break up the lumps.

Mix base

In a large bowl, beat the softened cream cheese until smooth. Add mayonnaise and sour cream and whisk until homogeneous and creamy.

Add cheeses and seasonings

Fold in the shredded cheddar and grated Parmesan, Worcestershire sauce, Dijon, lemon juice, Old Bay, black pepper, chives, and parsley. Taste and adjust seasoning (add up to 1/4 tsp more salt if needed).

Fold in crab

Gently fold the prepared jumbo lump crab meat into the mixture, taking care to keep lumps intact. Transfer the mixture to a 1 to 1.5-quart shallow ovenproof baking dish and smooth the top.

Topping

Preheat the oven to 375°F (190°C). In a small bowl, combine panko breadcrumbs, melted butter, and the extra shredded cheddar. Sprinkle evenly over the top of the crab dip.

Bake the dip on the center rack for 18–22 minutes, until bubbling around the edges and the topping is golden brown. If you want a deeper brown top, broil on high for 1–2 minutes while watching closely.

Toasted Bread

While the dip bakes, slice the baguette on a diagonal into 1/2-inch thick slices. Place slices on a baking sheet.

Brush both sides lightly with olive oil and sprinkle with sea salt and black pepper.

Toast in the oven at 375°F for 6–8 minutes (or under the broiler 1–2 minutes per side) until crisp and golden. Remove and let cool slightly.

Serve warm: place the baked crab dip on a platter and arrange toasted bread slices around it. Garnish dip with a few extra chopped chives or parsley if desired.