1Roast the peppers: Preheat oven to 400°F and line a baking sheet with parchment paper. Cut the very top of the peppers off and remove the stems, seeds and membranes. Lay the peppers on the baking sheet, cut side down. Roast the red peppers for 25-30 minutes, or until the skins are very dark and have collapsed.
2Boil the pasta: Bring a large saucepan of water (about 4 quarts) to a rolling boil and season with salt. Add the pasta and bring back to boil. Stir occasionally until the pasta is cooked to al dente according to package instructions, about 9 to 10 minutes. Reserve 1 cup of the pasta cooking water before draining.
3Soften the garlic: While the pasta is cooking, heat EVOO over medium heat until just shimmering. Add the garlic and stir until fragrant, about 30 seconds. Transfer the garlic and EVOO to the bowl of a large food processor fitted with a blade.
4Add the roasted peppers: Remove the skin from the red peppers completely, then cut the peppers into small pieces. Add the peppers to the food processor, along with the milk, oregano, paprika, and a big pinch of salt and pepper. Blend until smooth.
5Combine the pasta and sauce: When the pasta is ready, remember to reserve about 1 cup of the cooking water and drain. Return the pasta to the saucepan and pour the sauce on top. Turn the heat to low and add the parmesan. Stir to mix well so the pasta is fully coated in the sauce. Mix in the reserved pasta water, a splash at a time, as necessary until the pasta is glossy (you likely won't need all of the water). Top with parmesan and basil.