Preheat the oven to broil. Use an oven-safe skillet for cooking.
Pat the 4 salmon filets dry and season both sides with salt and black pepper. Place the salmon in the skillet. Dot the salmon with 1 tablespoon salted butter, scatter the 2 tablespoons fresh thyme leaves around the fish, and add the 4 lightly smashed garlic cloves to the skillet. Broil 5–8 minutes, watching closely, until the tops begin to brown and crisp.
Remove the skillet from the oven. Transfer the salmon to a plate and set aside, leaving the thyme and garlic in the skillet.
Place the skillet on the stovetop over medium heat. Add the remaining 3 tablespoons salted butter, the thinly sliced shallot, and chili flakes (to taste). Cook until the shallot is softened and fragrant, about 1–2 minutes. Use a fork to press the broiled garlic cloves in the skillet into a paste and stir to combine with the shallots.
Pour in 1 cup heavy cream and 1/3 cup salsa verde. Bring the mixture to a gentle simmer over medium heat, stirring constantly until smooth and slightly thickened.
Stir in 1 cup grated Parmesan cheese until melted and the sauce is creamy. Add 1/2 cup chopped sun-dried tomatoes and 3 cups fresh baby spinach; cook, stirring, until the spinach is wilted, about 3–5 minutes.
Slide the reserved salmon back into the skillet, nestling each filet into the sauce. Spoon sauce over the salmon and drizzle with 1 tablespoon lemon juice. Warm everything together 1–2 minutes so the salmon finishes cooking through and is heated.
In a small bowl, mix 1 tablespoon lemon zest with 2 tablespoons chopped fresh dill and 1/4 cup chopped green onions. Sprinkle this mixture over the salmon. Serve the salmon plated with the creamy sauce.