Preheat the broiler.
Make the breadcrumb topping: In a bowl, combine the butter and bread crumbs. Use a rubber spatula to mix them until they form a paste. Stir in the Gruyere and Parmesan cheeses. Mix in the thyme, salt, and pepper.
Cook the scallops: Heat a large skillet over high heat and add the canola oil. Season the scallops with salt and pepper. When the oil begins to smoke lightly, add them to the pan. Cook for 30 to 45 seconds until the edges brown and then quickly remove them to a plate using tongs.
Cook the mushrooms: Add the shallots and garlic to the pan and season with salt and pepper. Cook over medium heat until translucent, 2 to 3 minutes. Add the mushrooms and cook until they soften and brown lightly, 2 to 3 minutes. Add the vermouth and simmer until virtually all the liquid has evaporated, 2 to 3 minutes. Add the heavy cream, stirring gently, and simmer until the mixture thickens, 5 to 7 minutes. Do not boil vigorously or the mixture risks separating. Taste for seasoning. Stir the scallops, lemon juice, and scallions. Remove the pan from the heat.
Broil the scallop: Transfer the sauce and scallops to a shallow ovenproof dish (or into clean scallop shells, if desired). Sprinkle the bread crumbs over the top and broil until browned, 1 to 2 minutes. The time may be slightly longer or shorter depending on how quickly the top browns. Watch carefully! Serve immediately.
Recipe from Old School Comfort Food: The Way I Learned to Cook. Copyright (c) by Alex Guarnaschelli. By arrangement with Clarkson Potter.