Charred Caprese Sandwich

Mix mayonnaise, mustard, and lemon juice in a small bowl; season with salt. Toss shallot, garlic, and vinegar in another small bowl; season with salt. Let sit 10 minutes. Drain, reserving shallots and vinegar separately in small bowls. Prepare a grill for medium-high heat. Brush cut sides of bread with 2 Tbsp. oil total and grill until lightly charred, about 2 minutes per side. (Or broil bread halves, cut side up, until lightly charred, about 2 minutes.) Season with salt; let cool. Heat a large cast-iron skillet over medium-high (you can do this directly on the grill grates or on a burner). Toss tomatoes with remaining 2 Tbsp. oil and cook, shaking pan often, until tomatoes are blistered and lightly charred, about 3 minutes. Add tomatoes to bowl with reserved vinegar; season with salt and pepper. Let cool slightly, then add basil, parsley, and lemon zest and toss gently to combine. Taste and season with salt and pepper as needed. Spread both halves of baguette with mayonnaise mixture. Top with mozzarella, tomato salad, and shallots, and sprinkle with red pepper flakes.