Preheat oven to 375 degrees. Brush 2 rimmed baking sheets with 1 teaspoon oil. Cut five 1/4-inch-thick rings of squash; cut remainder into 1/4-inch dice. Place squash on sheets. Toss with 1 teaspoon oil; sprinkle with 12 sage leaves. Bake until tender and just golden, 15 to 20 minutes. Let cool completely. Keep oven on.
Heat remaining teaspoon oil in a medium saucepan over medium heat. Add onion and garlic. Cook, stirring, until translucent, 3 to 5 minutes. quinoa and stock; bring to a boil. Cover; reduce heat. Simmer until liquid has been absorbed, about 15 minutes. Remove from heat. Let stand, covered, 2 minutes.
Stir together quinoa, diced squash, chopped sage, Parmesan, salt, and pepper in a medium bowl.
Coat a 9-inch glass pie plate with cooking spray. Arrange 6 sage leaves face down in plate; top with squash rings. Press quinoa mixture on top.
Bake 20 minutes. Let cool 5 minutes, then invert onto a serving platter. Serve wedges warm or at room temperature.