Prep the chicken: Pat the chicken dry.
Place each breast between plastic wrap and pound to about 3/4-inch thickness. Season both sides with salt, pepper, and a light sprinkle of Old Bay.
Make the crab topping: In a bowl, gently combine crab meat, mayonnaise, cream cheese, 1/2–3/4 tsp Old Bay, garlic powder, onion powder, lemon zest, 1 tbsp lemon juice, breadcrumbs, and chopped parsley. Taste and adjust seasoning.
If you want a firmer topping, mix in the egg.
Sear the chicken: Heat 1 tbsp oil and 1 tbsp butter in a large oven-safe skillet over medium-high heat. Sear chicken 2–3 minutes per side until golden. Remove to a plate.
Preheat oven to 375°F (190°C).
Sauté aromatics: In the same pan, lower heat to medium. Add a touch more butter if needed, then sauté the shallot for 2 minutes. Add minced garlic and cook 30 seconds until fragrant.
Deglaze: Pour in white wine (or broth).
Scrape up browned bits. Let it reduce by about half, 2–3 minutes. Stir in Dijon if using.
Build the sauce base: Add heavy cream and a pinch of Old Bay.
Simmer 1–2 minutes to thicken slightly. Return chicken to the pan, nestling it into the sauce.
Top with crab: Mound the crab mixture evenly over each chicken breast, pressing gently so it adheres. Dot the tops with small bits of butter for extra richness.
Bake: Transfer skillet to the oven.
Bake 10–14 minutes, until the chicken reaches 165°F (74°C) in the thickest part and the crab topping is set and lightly golden at the edges.
Finish with lemon and butter: Remove from oven. Stir a squeeze of lemon juice into the pan sauce. If you want it silkier, whisk in 1 tbsp cold butter.
Spoon sauce around the chicken.
Garnish and serve: Top with chopped parsley or chives. Serve with mashed potatoes, rice, or roasted asparagus. Spoon extra sauce over everything.