Put the pizza dough in a large bowl and coat with 2 tablespoons of the olive oil. Cover the bowl with plastic wrap and let sit in a warm spot until the dough is slightly puffy, 30 minutes.
Spread the butter all over the inside of a metal 9-by-13-inch pan and put the dough in the middle. Starting from the middle of the dough and using your fingertips, push the dough out to the corners of the pan. Cover with plastic wrap and place in a warm spot until puffy and doubled in thickness, about 1 hour. Push the dough all the way to the edges, recover with plastic wrap and let rest for 15 minutes more.
Meanwhile, position an oven rack in the bottom third of the oven and preheat to 500 degrees F. Place a baking sheet on the rack to preheat.
Combine the tomatoes and tomato paste in a blender and blend until smooth. Heat the remaining 1 tablespoon olive oil in a large skillet over medium-high heat until shimmering. Add the garlic and cook until fragrant and soft but not brown. Add the tomato mixture, oregano, chile flakes, 1/2 teaspoon salt and 1/4 cup water, bring to a simmer, reduce the heat to medium low and cook until thick, about 15 minutes.
Uncover the dough and cover evenly with the pepperoni. Sprinkle about 2 cups of the Cheddar evenly along the edges of the pizza. Sprinkle the remaining 1/2 cup Cheddar over the rest of the pizza, then top the entire pizza with the Havarti and scallions.
Put the pan on the preheated baking sheet and bake the pizza until the edges are golden and the cheese is melted and bubbling, about 15 minutes.
Loosen the sides and bottom of the pizza with a metal spatula and slide onto a cutting board. Spoon the sauce in 4 thick crosswise lines over the pizza. Cut into squares and serve.
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