Remove the roasted peppers from the jar and measure out 6 oz; puree those 6 oz in a blender or with a hand chopper until smooth. Chop the remaining 6 oz of peppers and set both aside.
Pat the salmon fillets dry and season both sides with 1/2 tsp salt and 1/2 tsp paprika (or to taste).
Heat 2 tbsp olive oil in a large non-stick skillet over medium-high heat. When hot, add the salmon and cook 4–5 minutes per side, depending on thickness, until just cooked through. Remove salmon from the skillet and set aside.
Reduce heat to medium, add the diced onion and minced garlic to the same skillet, and cook, stirring, about 2 minutes until fragrant. Add 1/4 cup vegetable broth and continue cooking until the liquid mostly evaporates and the onions are softened.
Add the chopped peppers and pureed peppers to the skillet and cook, stirring occasionally, 5–7 minutes until the mixture thickens and the peppers become sweeter.
Lower the heat to low, pour in 3/4 cup heavy cream and add 1/2 cup shredded Parmesan and 1/4 tsp red pepper flakes. Stir to combine and bring to a gentle simmer. Taste and adjust seasoning with salt and pepper if needed.
Return the salmon to the skillet, spoon sauce over each fillet, and simmer covered for about 1 minute just to heat through. Sprinkle with 3 tbsp chopped parsley and serve.
