For the filling, combine mayonnaise, cracker crumbs, Parmesan, parsley, dry mustard, Old Bay, Worcestershire, and lemon juice. Gently fold in the crabmeat.
Heat oil in a sauté pan over medium-high until shimmering. Sear filets 5–6 minutes per side. Allow to cool on a rack for 15–20 minutes.
Preheat oven to 400°F. Arrange a wire rack inside a baking sheet.
Cut an “X” into the top of each filet to create a pocket. Carefully expand the pocket by snipping the tips of the “X”.
Stuff 1–2 Tbsp. of filling into each pocket, then top each filet with about ⅓ cup more filling.
Roast on the prepared baking sheet for 20 minutes for rare. Let rest 5 minutes before serving with Béarnaise Sauce.