1. Heat broiler and adjust the oven rack so its about 4 inches from heat source. Brush a baking sheet with olive oil. Put tomatoes cut sides up on baking sheet. If they wont lie flat, use a spatula or your hand to gently press them until stable. Sprinkle with salt and pepper.
2. Crumble blue cheese into large pieces, flatten them a bit with your fingers and put the pieces on top of tomatoes. Broil for 3 to 4 minutes, until cheese is golden and bubbly. Remove from oven and let tomatoes cool down in the pan for a bit to set.
3. Divide lettuce leaves among 4 serving plates. Top each with three tomato halves, drizzle with vinaigrette, garnish and serve. (Or arrange everything on one platter and serve family-style.)