Preheat broiler to high with oven rack in middle position.
Split each pita in half horizontally to get 12 rounds. Arrange rounds, cut side up, on a baking sheet; drizzle with 2 tablespoons oil. Broil 2 to 3 minutes or until lightly toasted.
Heat remaining 1 tablespoon oil in a large skillet over medium-high. Add shallots and garlic; sauté 2 minutes or until browned. Stir in kale; cook 2 minutes or until wilted. Remove pan from heat.
Spread about 2 teaspoons pizza sauce over each pita round; top evenly with kale mixture, cheeses, and tomatoes. Sprinkle evenly with pepper and salt. Broil 4 to 5 minutes or until cheeses are melted.
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