6 plum tomatoes, halved lengthwise
2 tablespoons olive oil, plus more for one of the baking sheets
3/4 teaspoon dried tarragon
Coarse salt and ground pepper
1/3 cup mayonnaise
1 tablespoon fresh lemon juice
3 slices white sandwich bread (about 1 ounce each), torn into large pieces
4 flounder fillets (1 1/2 pounds total)
2 tablespoons Dijon mustard
Preheat oven to 450, with racks in upper and lower thirds. Place tomatoes on a rimmed baking sheet. Sprinkle with 1 tablespoon oil, teaspoon tarragon, sugar, salt, and pepper; toss to coat. Arrange tomatoes cut side up. Roast on lower rack until tender, 20 to 25 minutes. (Keep oven on for fish.)
Meanwhile, make sauce: In a small bowl, whisk together mayonnaise, remaining 1/2 teaspoon tarragon, and lemon juice; season with salt and pepper. Set aside.
Line a rimmed baking sheet with aluminum foil and brush with oil. In a food processor, place bread, a pinch each salt and pepper, and remaining tablespoon oil; pulse until fine crumbs form.
Lay fillets flat on prepared baking sheet; season with salt and pepper. Spread top sides with mustard; sprinkle with bread crumbs, pressing to adhere. Bake on upper rack until fish is cooked through and crumbs are browned, 6 to 8 minutes. Serve with tomatoes and sauce.