Heat oven to 400º F. Toss the tomatoes with 1 tablespoon of the
olive oil and 1/4 teaspoon of the salt. Arrange the tomatoes, cut-side up, on a baking sheet. Bake until they are just softened, about 10 minutes. Meanwhile, whisk together the Feta, yogurt, lemon juice, and 1/4 teaspoon of the salt; set aside. Place a medium skillet over medium heat. Add 1/2 tablespoon of the olive oil to the skillet. Add the garlic and red pepper flakes. Cook, stirring occasionally, until the garlic is softened and just turning golden. Add the spinach and the remaining salt. Cook, tossing occasionally, until the spinach is just wilted, about 4 minutes. Brush both sides of the pitas with the remaining olive oil. Place in the oven and heat until lightly toasted, about 2 minutes per side. (You can also do this on a medium-hot grill.) Place the pitas on plates. Top with the spinach and tomatoes. Drizzle the yogurt-Feta sauce on top and serve.