How to Make It
Preheat the oven to 375°. Brush a large rimmed baking sheet with 2 teaspoons of the olive oil. Lay 1 sheet of the phyllo dough on the baking sheet; keep the rest covered with damp paper towels. Brush the phyllo with 2 teaspoons of olive oil and sprinkle all over with 1 tablespoon of the breadcrumbs. Repeat the layering with the remaining phyllo, olive oil and breadcrumbs.
Bake the crust for about 25 minutes, until golden and crisp; rotate the baking sheet halfway through cooking. Let cool completely.
In a food processor, pulse the cream cheese with the mayonnaise until smooth. Spread the cream cheese mixture in the center of the tart, leaving a 1/2-inch border all around. Arrange the tomato slices on top and sprinkle with flaky sea salt and pepper. Drizzle lightly with olive oil and garnish with basil leaves. Cut into squares and serve.