Step 1

Mix mayonnaise, mustard, and lemon juice in a small bowl; season with salt.

Step 2

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.

Step 3

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.

Step 4

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.

Step 5

Spread both halves of baguette with mayonnaise mixture. Top with mozzarella, tomato salad, and shallots, and sprinkle with red pepper flakes.

Step 6

Mayonnaise can be made 3 days ahead. Cover and chill.