Meanwhile, halve the tomatoes. Heat the olive oil in a large skillet over medium-high heat. Add the tomatoes and cook until softened and begin to release their juices, 5 to 7 minutes. Add the garlic and cook until fragrant, about 30 seconds.

Transfer the tomatoes and garlic to a blender. Add 1 cup of the reserved pasta water and blend until smooth. Strain through a fine-mesh strainer, pressing on the solids, and discard the skins and seeds.

Return the tomato sauce to the skillet and season with salt and black pepper. Add the pasta and toss to coat.

Reduce the heat to low. Add the cold butter a few cubes at a time, tossing until melted and incorporated. Add the grated cheese and toss until the sauce is smooth, glossy and thick enough to coat the pasta. Add more pasta water as needed.

Divide the pasta among bowls. Top with Pecorino or Parmesan, lemon zest, za’atar and Aleppo pepper. Finish with black pepper and serve immediately.