Bring a large pot of generously salted water to a boil and add your pasta. Cook it until it's just al dente, since it will finish cooking briefly in the sauce later. Before draining, scoop out a cup of the starchy pasta water and set it aside for later use.
Tip the jarred roasted red peppers into a strainer and squeeze out as much of the brine as you can with your hands. Don't rinse them under water, since that brine carries a lot of the flavor the sauce needs. Just get rid of the excess liquid.
Melt the butter in a large deep pan over medium heat and add the diced onion. Cook until soft and lightly golden, then stir in the garlic for another minute or so. Keep an eye on the garlic so it doesn't catch and burn.
Scrape the butter, onion, and garlic straight into a blender along with the drained roasted red peppers. Blitz everything until completely smooth. If the mixture is too thick for your blender to handle, add a small splash of stock, milk, or water to loosen it up.
Pour the blended pepper mixture back into the pan and keep it on a low simmer. Stir in the room-temperature cream until it's fully combined and the sauce turns a soft coral color. Let it bubble gently for a minute or two.
Stir in the freshly grated parmesan, parsley, smoked paprika, chilli flakes, and a generous pinch of salt and pepper. Keep stirring until the cheese melts smoothly into the sauce and everything looks glossy and thick.
Use tongs to lift the pasta straight from the pot into the sauce, letting a little pasta water come along with it. Toss everything together until every strand is coated. If the sauce feels too thick, splash in more of the reserved pasta water until it loosens up.