Heat a large sauté pan over medium heat, add 3 tablespoons of butter and allow to melt. Add the mushrooms, onions, celery, and garlic and cook, stirring occasionally, until the vegetables have softened and the liquid the mushrooms give off is evaporated, about 6 minutes.
Add the crabmeat and half of the parsley, and stir gently on medium heat until combined but the crab remains in large pieces, about 1 minute.
Stir in the chicken stock and crushed cracker crumbs and remove from heat. Season with salt and pepper to taste.
Cut the shrimp from head to tail along the backside to butterfly the shrimp. Open each butterflied shrimp, so they are flat with the cut side facing up.
Scoop about 2 tablespoons of crab stuffing and shape into a ball. Place on a rimmed baking sheet and top with a butterflied shrimp, pressing gently to adhere. Melt the remaining 2 tablespoons of butter in a small bowl and brush or drizzle it on the shrimp and sprinkle the paprika over the top (if using).
Bake until the shrimp are pink and no longer translucent, about 18 to 20 minutes.
Serve the baked stuffed shrimp immediately topped with the remaining parsley and with the lemon wedges on the side.
Notes
This recipe has been tested using Ritz crackers. 30 crackers is about 1 sleeve of crackers. Using crackers instead of plain breadcrumbs will create a moist buttery flavor.