Bring a large pot of heavily salted water to a boil over medium-high heat. Meanwhile, thinly slice 6 large garlic cloves (about ¼ cup). Finely grate 1 ounce Parmesan cheese (about ½ packed cup) or measure out ⅓ cup store-bought grated.

Heat ⅓ cup olive oil in a large skillet over medium heat until shimmering. Add the garlic and ¼ teaspoon red pepper flakes and cook, stirring occasionally, until the garlic is softened and turns light golden-brown, about 2 minutes.

Add 1 (6-ounce) can tomato paste and ½ teaspoon kosher salt. Cook, stirring often, until the tomato paste is significantly darkened in color to a deep rusty red, caramelized in a few spots, and starts to stick to the bottom of the pan, about 5 minutes. Remove the pan from the heat.

Meanwhile, add 1 pound dried pasta to the boiling water and cook according to package directions until 1 minute less than al dente. Reserve 2 cups of the cooking water. Drain the pasta.

Add the pasta water to the skillet and stir to combine with the tomato paste mixture (a few lumps are fine — it will smooth out when the mixture simmers). Bring to a simmer over medium-high heat. Simmer until the liquid reduces and thickens slightly, about 1 minute. Add the pasta and toss continuously until the sauce thickens a bit more and coats the pasta, and the pasta is al dente, about 1 minute more.

Remove the pan from the heat. Add half of the Parmesan and toss to combine. Serve garnished with the remaining Parmesan and chopped fresh parsley leaves and more red pepper flakes if desired.