Pound each chicken breast between plastic wrap to an even 3/4-inch (2cm) thickness. Pat dry, season both sides with salt, pepper, garlic powder, and paprika, then let rest at room temperature for 10–15 minutes.
Preheat oven to 375°F (190°C). Heat olive oil in an oven-safe skillet over medium-high heat, then sear chicken 4–5 minutes per side until golden. Remove to a plate and set aside.
In the same skillet over medium heat, melt butter and sauté garlic 30–45 seconds. Add wine, lemon juice, and Old Bay, then gently fold in crab meat and cook 2–3 minutes until heated through. Remove from heat.
In a saucepan, melt butter, whisk in flour, and cook 1–2 minutes until golden. Gradually whisk in heavy cream and chicken broth, simmer 3–4 minutes until thickened, then stir in Dijon mustard, nutmeg, and salt and pepper to taste.
Return chicken to the skillet, spoon crab mixture over each breast, drizzle cream sauce over the top, and sprinkle generously with shredded Gruyère cheese.
Bake at 375°F (190°C) for 15–18 minutes until chicken reaches 165°F (74°C) internally and cheese is melted and bubbly. Broil for 1–2 minutes for extra browning if desired.
Rest for 5 minutes, then garnish with fresh parsley and serve with lemon wedges and extra cream sauce spooned around the plate.