Cut the scallops in half (two half-circles) and transfer to a medium bowl; season with 1/2 teaspoon salt and a few grinds of pepper. Add the olive oil, thyme and parsley and toss to coat; cover and refrigerate until ready to cook.
Generously butter the insides of the rolls. Heat a large skillet over medium heat. Add the rolls, buttered-side down, and toast until golden, about 3 minutes. Remove to a plate and let cool, then tuck 2 lettuce leaves into each.
Heat the skillet over medium-high heat and add the scallops in a single layer. Cook, undisturbed, until golden on one side, about 3 minutes. Flip the scallops and add the remaining 3 tablespoons butter to the pan, swirling to distribute the butter. Tilt the pan slightly and spoon the butter over the scallops until they are cooked through and the butter begins to brown and smell nutty, about 3 more minutes. Add the lemon juice and toss.
Divide the scallops among the rolls and drizzle with the browned butter. Sprinkle with the chopped herbs and serve with lemon wedges.