Preheat oven to 325°F (160°C) and set rack to middle position. In a large pot of salted boiling water, cook shells according to package instructions for baked shells, about 3 minutes less than the package's recommended cooking time. Transfer shells to a bowl of cold water to cool slightly, then drain. Drizzle with oil and toss to coat.
Fill a large bowl with ice water. Poach shrimp in the same pot of pasta water until just barely cooked through, 1 to 2 minutes. Drain, chill in ice bath, then drain again. Chop shrimp into small pieces.
In a mixing bowl, combine crabmeat with shrimp, scallops, Dijon, mayo, Old Bay, shallot, and parsley. Mix well and season with salt and pepper.
In a small saucepan, melt 1 ½ tablespoons of butter over medium-high heat. Add flour and whisk to form a paste. Cook, stirring, until raw flour scent is gone, about 1 minute. Gradually whisk in milk, stirring until sauce thickens slightly, then add bay leaf.
Reduce heat to low and cook, stirring, until sauce is thick enough to lightly coat the back of a spoon, about 3 minutes. Season with salt and pepper and discard bay leaf.
Lightly grease a baking dish with oil. Spread ½ cup béchamel sauce in an even layer on the bottom. Fill shells with the seafood mixture and place in the dish opening side up, about 18 shells.
Spoon remaining 1 cup béchamel sauce on top. Melt remaining 2 tablespoons of butter and mix with breadcrumbs. Season with salt and sprinkle over the shells.
Bake shells until heated through, about 25 minutes. Switch oven to broiler and broil until breadcrumbs are golden, watching closely. Garnish with minced parsley and serve.