Position a rack in the center of the oven; preheat to 450 degrees . In a large nonstick skillet, heat 1 tbsp. oil over medium. Add the garlic and crushed red pepper and cook, stirring often, until the garlic begins to brown at the edges, 1 to 1 1/2 minutes. Add the fennel and oregano and cook, stirring often, until the fennel softens slightly, 3 to 4 minutes. Stir in the kale; cook until just wilted, about 1 minute. Season with salt.
Brush the remaining 1 tbsp. oil on a pizza pan or large baking sheet and stretch the dough over it. Sprinkle with 1 cup mozzarella, leaving a 3/4-inch border around the edges. Top with the kale mixture, then sprinkle with the remaining 1 cup mozzarella and the Parmesan.
Bake until the edges of the dough are lightly golden and the cheese is browned in spots, 16 to 18 minutes.