For the Crab Cakes

For the Sauce

For the crab cakes: Combine stock, cream, and sherry in a saucepan and simmer over medium-high heat until reduced to about ¹⁄₂ cup, about 40 minutes. Set aside to cool.
Combine celery, onions, parsley, egg yolks, bread crumbs, and cooled cream mixture in a large bowl. Fold in crab, then shape into 8 crab cakes about 3" in diameter. Arrange on a plate, cover, and refrigerate for 4 hours or overnight.
Preheat oven to 350°. Dredge crab cakes in flour and shake off excess. Heat oil in a large skillet over medium-high heat. Working in batches, fry crab cakes, turning once, until browned, about 1 ¹⁄₂ minutes per side. Transfer with a slotted spatula to a baking sheet. Bake until heated through, 5–10 minutes.
For the sauce: Sauté shallots in the same skillet for 1 minute. Add cream, stock, and sherry, and boil until thickened, about 1 minute. Remove from heat and whisk in butter one piece at a time. Add parsley and season to taste with salt and pepper. Divide sauce among four plates and place 2 crab cakes on top of sauce on each plate. Serve with Crab Salsa and boiled shrimp, if you like.