Serving the oysters and clams atop rock salt ensures that they stay upright -- and also makes a striking presentation.
Tear bread slices into pieces and place in the bowl of a food processor. Pulse until coarse crumbs form (you should have about 2 cups).
Preheat broiler with rack 6 to 7 inches below heating element. Arrange shellfish in a single layer on a rimmed baking sheet. Broil just until shells begin to open, 4 to 6 minutes.
When cool enough to handle, remove top shells, taking care not to get any shell in meat, and discard. Tip out any oyster and clam liquor still in shells onto baking sheet. Loosen meat from shells with an oyster knife; transfer (still in shells) to another parchment-lined rimmed baking sheet. Strain shellfish liquor from first sheet through a fine-mesh sieve into a measuring cup. Fill shells with liquor (you may not need it all).
Melt butter in a large skillet over medium. Add garlic and bell pepper; saute until fragrant, about 1 minute. Add vermouth; boil until mostly evaporated. Add breadcrumbs and oregano; cook, stirring occasionally, until breadcrumbs turn golden and crisp in places, about 3 minutes. Remove from heat. Stir in parsley and cheese; season with pepper. Divide breadcrumb mixture evenly among shellfish, then top evenly with pancetta.
Broil just until crisp and golden brown on top, 2 to 4 minutes. Serve warm on a platter lined with rock salt.