Make the crab filling. In a mixing bowl, combine the crab, shallot, ritz crackers, mayo, old bay, lemon zest, dijon, and chopped parsley. Use a rubber spatula to fold everything together until it’s well mixed. Season with kosher salt and freshly cracked pepper. Set aside.
Make the old bay butter. Melt the salted butter in a small saucepan until the butter is foamy. Add the old bay, grated garlic, and lemon zest and stir well. Cook for 1 minute, then remove the butter from the heat.
Prep the salmon. Line a baking sheet with parchment paper. Pat the salmon filets dry and season them on both sides with salt and pepper. Place them evenly spaced on the prepared baking sheet. Use a sharp knife to cut a slit across the top of each filet lengthwise to create a pocket (don’t slice all the way through the salmon).
Preheat an oven to 425°F.
Stuff the salmon. Divide the crab into 4 portions and stuff each salmon filet with the crab mixture, mounding it on top. Use half of the old bay butter to liberally brush the top of each salmon filet.
Bake. Bake the salmon for 16-20 minutes (depending on size of salmon filets used), until the salmon is opaque and the crab is warmed through, with an internal temperature of 145°F. Remove from the oven and drizzle with the rest of the old bay butter. Squeeze with fresh lemon before serving.