Cook 12 oz. medium pasta (such as gemelli or fusilli) in a large pot of boiling salted water, stirring occasionally, until al dente. Drain and rinse under cold running water to remove excess starch.

Meanwhile, heat ½ cup extra-virgin olive oil in a skillet over medium-high. Add 3 Tbsp. pine nuts and 2 Tbsp. drained capers; cook, stirring often, until nuts are golden brown and capers are crisp, about 3 minutes. Using a slotted spoon, transfer fried nuts and capers to paper towels and let drain.

Add 1 large onion, thinly sliced, and 4 garlic cloves, finely chopped, to same pan and season with 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt. Stir to combine, then cook, stirring often, until onion starts to soften and garlic is fragrant, about 3 minutes. Add 2 Tbsp. double-concentrated tomato paste and ½ tsp. crushed red pepper flakes and cook, stirring occasionally, until tomato paste is slightly darkened in color, about 4 minutes. Transfer onion mixture to a large bowl and let cool 5–10 minutes.

Add pasta, 1 bunch parsley, leaves and tender stems coarsely chopped, ½ cup Castelvetrano olives, pitted, smashed, halved, ½ cup chopped oil-packed sun-dried tomatoes, 2–3 tsp. finely grated lemon zest, 3 Tbsp. fresh lemon juice, and remaining 2 Tbsp. drained capers to onion mixture and toss to combine. Taste and add more lemon juice and season with more salt if needed.

To serve, top pasta salad with fried pine nuts and capers. Sprinkle with more red pepper flakes and drizzle with oil. Do ahead: Pasta can be cooked 3 days ahead; transfer to an airtight container and chill. Pine nuts and capers can be fried 1 day ahead; store airtight at room temperature separately. Salad (without toppings) can be assembled 8 hours ahead; cover and chill.