Bring a large pot of salted water to a boil. Salt generously — it should taste like seasoned broth.
Drain sun-dried tomatoes, reserving 3 tablespoons of the packing oil. Roughly chop tomatoes.
Heat reserved oil in a large skillet over medium heat. Cook onion 5 minutes until soft.
Add garlic, red pepper flakes, oregano, and smoked paprika. Cook 1–2 minutes until fragrant.
Add chopped sun-dried tomatoes. Stir and cook 2 minutes, pressing gently to break down slightly.
Pour in vegetable broth. Simmer 3–4 minutes until slightly reduced.
Cook pasta until just under al dente — 1 minute less than the package says.
Before draining, scoop out at least 1 cup of pasta water and set aside.
Drain pasta and add directly to the skillet. Add butter and ½ cup pasta water.
Toss vigorously over medium heat for 2 minutes until sauce is glossy and clings to pasta.
Remove from heat. Add Parmesan and toss until fully melted.
Taste and adjust salt, pepper, and chili flakes.
Serve in warm bowls topped with torn basil, extra Parmesan, and a drizzle of olive oil.