Stir in tomatoes and sugar, increase heat to high, and bring to a simmer. Lower heat to medium-low and simmer until reduced to about 2½ cups, 25 to 30 minutes. Off the heat, stir in the basil and olive oil, then season with salt and pepper.
Laminate the Dough: Turn the dough out onto dry work surface and roll into a 15×12-inch rectangle. Using an offset spatula, spread the softened butter over the surface of the dough, leaving a ½-inch border along the edges. Starting at the short end, roll the dough into a tight cylinder. With seam side down, flatten the cylinder into an 18×4-inch rectangle.
Cut the rectangle in half crosswise. Working with one half, fold into thirds like a business letter; pinch seams together to form a ball. Repeat with the remaining half. Return balls to the oiled bowl, cover tightly with plastic wrap and let rise in refrigerator until nearly doubled in volume, 40 to 50 minutes. Meanwhile, adjust oven rack to lower position and preheat oven to 425 degrees F.

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