To prepare filling, place colander in a 2-quart glass measure or medium bowl. Line colander with 4 layers of cheesecloth, allowing cheesecloth to extend over outside edges. Spoon yogurt into colander. Cover loosely with plastic wrap; refrigerate 12 hours. Spoon 1 3/4 cups yogurt cheese into a bowl; discard liquid. Place cream cheese in a bowl; beat with a mixer at medium speed until smooth. Add the yogurt cheese, ricotta cheese, 1/2 teaspoon salt, 1/4 teaspoon pepper, and egg yolk. Beat at low speed just until blended.
Preheat oven to 350º.
To prepare crust, lightly spoon flour into a dry measuring cup; level with a knife. Place flour, cornmeal, 1 teaspoon sugar, 1/2 teaspoon salt, and dash of pepper in a food processor; pulse 3 times or until combined. Add 2 1/2 tablespoons butter; pulse 4 times or until mixture resembles coarse meal. With processor on, add ice water through food chute, processing just until moist (do not form a ball). Press cornmeal mixture into bottom of an 8-inch springform pan coated with cooking spray. Bake at 350º for 15 minutes or until lightly browned. Cool on a wire rack.
To prepare onions, while crust bakes melt 1 teaspoon butter in a large nonstick skillet over medium heat. Add the onion; cook 15 minutes, stirring occasionally. Stir in 1 tablespoon sugar, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Cover and cook 25 minutes or until browned and tender, stirring occasionally. Stir in thyme.
Spread the yogurt mixture into prepared crust. Bake at 350º for 35 minutes or until almost set. Cool on a wire rack. (Cheesecake will continue to set as it cools.) Serve at room temperature. Cut cheesecake into wedges, and serve with onions.