Start the pasta: Bring a pot of salted water to a boil and cook pasta until al dente. Reserve ½ cup pasta water, then drain.
Season the salmon: Pat 4 salmon fillets (6 oz each, about 1 inch thick) very dry. Brush with about 1 tbsp of the 2 tablespoons olive oil, divided, then coat the tops and sides well with 2 tbsp Trader Joe's Salmon Rub (use a little less for fillets; homemade blend in notes). Fillets need a little less rub than bites. (Making bites or using the stovetop? See the notes.)
Air fry the salmon: Preheat the air fryer to 380°F. Place fillets in a single layer (skin-side down if skin-on) with space between them. Air fry 8 minutes.
Build the sauce: While the salmon cooks, heat the remaining 2 tbsp olive oil, divided in a large skillet over medium heat. Sauté 5 garlic cloves, minced for 30–60 seconds until fragrant, then add sun-dried tomatoes in oil, drained and chopped and cook 1–2 minutes.
Simmer: Stir in chicken or vegetable broth (or reserved pasta water) and half and half. Bring to a gentle simmer, not a hard boil, and cook 3–4 minutes until slightly thickened.
Finish the sauce: Reduce heat to low and stir in freshly grated parmesan a handful at a time until melted. Remove from heat, then stir in fresh lemon juice, red pepper flakes (optional) if using, and most of the fresh basil, thinly sliced. Taste before adding salt for the sauce, only if needed after tasting; the parmesan, broth, and rub may already be salty enough. Loosen with reserved pasta water if needed.
Combine and serve: Toss the pasta with about half the sauce. Top with the salmon, spoon the remaining sauce over, and garnish with the rest of the basil.