Place all dressing ingredients — 1 ½ cups basil, 1 chopped shallot, 1 clove chopped garlic, ½ cup EVOO, 2 Tbsp lemon juice, 1 tsp white wine vinegar, 1 tsp Kosher salt, and a pinch of red pepper flakes — in a blender, then purée until very smooth. Set aside.
Place sliced tomatoes or wedges on a large platter or serving plate. Add halved cherry or grape tomatoes, then season the tomatoes with a few generous pinches of flaky sea salt. Let the tomatoes sit. Scatter the mozzarella pieces on top.
Drizzle as much of the lemon basil vinaigrette on top of the tomatoes and mozzarella. Season with freshly ground black pepper, if using, then garnish with a few small basil leaves. Serve immediately.