How to Make It
Heat oven to 450° F. Heat 2 tablespoons of the oil in a large skillet over medium-high heat. Add the onion, garlic, and ½ teaspoon each salt and pepper and cook, stirring occasionally, until softened, 3 to 5 minutes. Add as much kale to the skillet as will fit and cook, tossing frequently and adding more kale when there is room, until tender, 4 to 6 minutes. Transfer to a large bowl and let cool.
Divide the dough into 2 pieces. On a lightly floured surface, roll and stretch each piece of dough into a large oval. Transfer to 2 lightly oiled baking sheets.
Dividing evenly, brush the dough with the remaining tablespoon of oil and top with 1 cup of the Cheddar; top with the tomatoes, kale mixture, and the remaining cup of Cheddar. Bake, rotating the sheets halfway through, until golden, 15 to 18 minutes.