How to Make It
Preheat oven to 450°F with a rack in lowest position. Arrange tomatoes on a large baking sheet lined with paper towels. Season with 1 teaspoon salt and let stand 10 minutes. Pat dry with paper towels.
Meanwhile, stir together cheese, mayonnaise, scallions, chopped dill, cayenne, and ¼ teaspoon pepper in a medium bowl. Place oil in a small bowl. Line a baking sheet with parchment paper, brush with oil, and place 1 phyllo sheet on top; brush with oil. Repeat with remaining 9 phyllo sheets and oil. Spread cheese mixture evenly over top, leaving a ½-inch border. Top with tomatoes and season with remaining ¼ teaspoon each salt and pepper.
Bake until crust is golden brown, 18 to 20 minutes; let cool 5 minutes. Top with dill sprigs just before serving.