In a skillet or pot with a tight-fitting lid, heat 3 tbsp. EVOO, 3 turns of the pan, over medium heat. Melt the anchovies into the oil, then stir in the chile and garlic for 2 to 3 minutes. Stir in 1/4 cup vermouth (or white wine), then the tomatoes and capers. Cover the pan, increase the heat and cook, shaking the pan occasionally, until the tomatoes burst, about 15 minutes. Break up the burst tomatoes a bit with a wooden spoon, then remove the pan from the heat.
When the sauce is about done, in a large skillet, heat the remaining 2 tbsp. EVOO, 2 turns of the pan, over medium-high heat. Add the shrimp and season with sea salt and pepper; toss until firm and opaque, 3 to 5 minutes. Pour in the remaining 1/4 cup vermouth (or white wine) to deglaze the pan. Add the butter to melt, then stir in the lemon juice and parsley.
Pile some lettuce into the warm rolls. Top with the shrimp and lots of sauce.