Cook the clams: Heat a large skillet over high heat. Rinse the clams one final time to make sure they are free of any grit. Add 1 tablespoon of the butter to the skillet, add the clams and vermouth and cook, shaking the skillet slightly, until the clams open. Remove and cool. Reserve any cooking liquid.
Make the breadcrumb mix: Place the remaining 10 tablespoons butter in the bowl of a food processor, add the garlic, scallions and lemon zest and juice and pulse to blend. Transfer the mixture to a bowl and season with salt and pepper. Mix in the breadcrumbs.
Prepare and bake the clams: Detach each clam from its shell and put the meat back in the shell. Mix the reserved cooking liquid from the clams (if any) with the cream. Pour a touch of the cream mixture on top of each clam and immediately mold some of the breadcrumb mixture into each of the shells so the clam body is covered. Arrange them in a single layer on a baking sheet. Bake until hot, 10 to 12 minutes. Remove from the oven and preheat the broiler.
Broil the clams for 1 minute, watching them constantly so they don't burn. Remove them from the oven. Squirt with lemon juice. Top each clam with some parsley. Serve immediately.