Preheat oven to 325˚F. Line 2 sheet pans with parchment paper.
Spread tomatoes out in a single layer on one of the prepared pans. Drizzle tomatoes with 3 tablespoons oil and 1 ½ tablespoons balsamic vinegar. Sprinkle with 1 teaspoon sugar, ½ teaspoon sea salt and a generous grind of freshly ground black pepper.
Spread mushrooms halves out in a single layer on the second prepared pan. Drizzle mushrooms with 3 tablespoons oil and 1 tablespoon balsamic vinegar. Sprinkle with ½ teaspoon sugar, ½ teaspoon sea salt and a generous grind of freshly ground black pepper.
Roast tomatoes and mushrooms for 60-75 minutes or until most of the liquid has disappeared. Gently stir every 15 minutes during roasting time. Mushrooms will be finished about 10-15 minutes before tomatoes. Remove from oven when veggies are deep golden and caramelized. Set aside, but leave oven on.
Brush both sides of bread slices lightly with olive oil. Place in a sauté pan and cook over medium heat until golden on both sides. Cook in batches, if needed. Place bread slices on a sheet pan.
Top each bread slice with 1 ½ tablespoons pesto. Spread pesto to edges of bread slices. Slice or tear mozzarella in to small pieces. Top pesto layer with torn mozzarella. Add tomatoes and mushrooms, dividing evenly between the tartines. Return to oven and bake till cheese is melted, about 6-8 minutes.. Scatter with fresh basil leaves and serve.