Blend the peppers. Blend the roasted peppers in a food processor or blender until smooth.
Boil the pasta. Bring a large pot of water to a boil and salt it generously. As soon as the water boils, add the pasta and cook for 1 minute less than the package directions, stirring occasionally so it doesn’t stick. It will finish cooking in the sauce. While the pasta boils, work on the sauce. When the pasta is cooked, drain it, reserving 1 cup of pasta water.
Start the sauce. When you add the pasta to the pot to boil, start the sauce. Set a large skillet over medium heat and add the butter. Once it has melted, add the shallot and a pinch of salt and sauté, stirring often, for about 2 minutes, until soft and translucent but not browned. Add the garlic and stir constantly for 30 seconds, just until fragrant. Don’t let it brown. Pour in the blended peppers and cook, stirring occasionally, for about 3 minutes, until the sauce darkens slightly and starts to bubble.
Continue making the sauce. Ladle 1/2 cup of water from the pasta pot into the sauce and keep cooking the sauce, stirring for about 3 minutes until reduced.
Combine the sauce with the pasta. Add the drained pasta and 1/4 cup of the reserved pasta water. Cook for 1 minute, stirring and tossing continuously so the sauce coats every piece. Add more pasta water if you need to loosen up the sauce. Turn off the heat.
Add the olives, artichokes, and parmesan. Stir until the parmesan has melted into the sauce.
Add the feta. Finally, add the feta and stir until well combined. Taste and adjust salt if needed (it likely will not need it due to the feta, parmesan, and olives).
Serve. Divide between bowls and serve right away, topped with extra feta, olives, and torn fresh basil if you like.