Combine the tomatoes, onion, mushrooms, and garlic in a saucepan. Cook over medium heat until the mixture is somewhat dry. Set aside to cool.
Combine the tomato mixture, spinach, cottage cheese, and basil in a large bowl. Add pepper to taste
On a cutting board, lay out a single layer of pot-sticker shells. Using a pastry brush, moisten the edges with water. Place 1 tablespoon of the spinach mixture onto the center of each shell. Cover with a second pot-sticker shell and press the edges together with a fork to seal. Repeat with remaining shells.
Cook the ravioli in boiling water for 3-4 minutes.