Pepper Pasta Salad

Preheat oven to 350°. Toast nuts on a rimmed baking sheet, tossing halfway through, until golden brown, 5–10 minutes depending on type of nuts. Let cool, then coarsely crush; set aside.

Meanwhile, cut bell peppers in half lengthwise through their stems. Remove and discard any seeds and white ribs. Cut large bell peppers into 1"-thick strips and baby bell peppers in half lengthwise. Thinly slice chiles crosswise into rounds; discard stems.

Heat oil in a large Dutch oven over medium-high until shimmering, about 3 minutes. Add peppers, chiles, garlic, thyme, 2 tsp. salt, and 1 tsp. sugar and cook, stirring occasionally, until peppers begin to soften and are golden brown in some spots, 10–15 minutes. Reduce heat to medium-low and add ½ cup vinegar. Partially cover pot and cook, stirring every 5–10 minutes, until peppers are very soft, jammy, and browning in some spots, 35–45 minutes longer. Remove from heat. Pluck out and discard any shriveled thyme stems.

While peppers cook, thinly slice onion and transfer to a small bowl. Add ½ tsp. salt and remaining 3 Tbsp. vinegar and 2 tsp. sugar, then toss to combine. Let sit to lightly pickle until ready to use.

Cook rigatoni in a large pot of boiling salted water, stirring occasionally, until al dente. Drain and add pasta to pot with peppers. Add pickled onions and their pickling liquid, then toss well to evenly coat pasta. Let cool to room temperature.

Crumble ricotta salata into pot, then stir in reserved nuts. Tear basil into coarse pieces, add to pot, and stir until combined.

Transfer to a large bowl and serve at room temperature, or cover and chill if you prefer to serve salad cold.

Do Ahead: Pasta salad can be made 3 days ahead. Let cool to room temperature, cover, and chill.