Preheat the barbecue or grill.
In a medium saucepan, heat 1-teaspoon oil. Sweat the shallots for about 2 minutes. Do not brown. Deglaze the pan with the wine and vinegar and reduce slightly. Pour in the cream and reduce the sauce by half. Whisk in the butter and strain into a clean pan. Season with lemon juice, salt, and pepper, to taste. Keep warm.
Sprinkle the 3 tablespoons vegetable oil over the shrimp. Grill the shrimp, about 1-1/2 minutes on each side. Do not overcook. Drain and cut each shrimp in half lengthwise.
For each sandwich, spread a little mayonnaise on 1 slice of bread and arrange a little lettuce (or 1 piece) on the bread. Top with 3 slices of tomato, season lightly with salt and pepper, and arrange the bacon on the tomatoes. Top with the second slice of bread, a thin layer of mayonnaise, and a little lettuce. Heat the shrimp (10 halves) in the lemon butter and arrange on the lettuce. Top with the third slice of bread and cut in half. Serve immediately.