Shuck oysters, reserving bottom shells and 1 Tbsp. oyster liquor (oyster liquid in shell); discard top shells. Gently loosen oyster from shell, using an oyster knife.
Preheat broiler with oven rack 6 inches from heat. Melt 1 Tbsp. butter with 1 Tbsp. olive oil in a large skillet over low heat; stir in breadcrumbs and next 9 ingredients. Remove from heat.
Microwave remaining 1 Tbsp. butter and 1 Tbsp. olive oil in a small microwave-safe bowl at HIGH 20 seconds or until butter melts. Stir in reserved oyster liquor.
Spread rock salt in a 1/4-inch layer in a 18- x 13-inch shallow pan. Place oysters, in shells, on rock salt. Spoon breadcrumb mixture over oysters; drizzle with butter mixture. Broil 5 to 6 minutes or until top is crisp and browned.
Broiled Oysters: Omit rock salt. Prepare recipe as directed, doubling ingredient amounts. Shuck oysters, discarding shells, and place oysters in a single layer in a 13- x 9-inch pan. (Pre-shucked oysters work well for this. Reserve 2 Tbsp. oyster liquor.) Top with breadcrumb mixture; broil.