Boil the pasta: Bring a large pot of salted water to a rolling boil. Cook the pasta until just shy of al dente.
Reserve 1 cup of the starchy cooking water before draining.
Prep the tomatoes: If using oil-packed sun-dried tomatoes, lift them from the jar and roughly chop. Reserve 2 tablespoons of the tomato oil. If dry-packed, soak them in warm water for 10 minutes, drain, and chop.
Sauté aromatics: In a large skillet, warm the reserved tomato oil (or olive oil) over medium heat.
Add garlic and red pepper flakes. Cook 30–60 seconds until fragrant, not browned.
Build the sauce base: Add the chopped sun-dried tomatoes and cook for 2 minutes. Stir in the broth (if using) and 1/2 cup pasta water.
Simmer for 2–3 minutes to meld flavors.
Add the pasta: Transfer the drained pasta to the skillet. Toss vigorously so the sauce coats every piece. Add more pasta water as needed to keep it glossy.
Finish with richness: Off the heat, stir in Parmesan until it melts into the sauce.
Add the butter if using. Season with salt and plenty of black pepper.
Brighten it up: Fold in lemon zest, a squeeze of lemon juice, and most of the basil. Toss again.
Adjust seasoning and heat level.
Top and serve: Sprinkle with capers and nuts if using. Garnish with the remaining basil and a little extra Parmesan. Serve immediately.