Prepare the garlic emulsion. I cut the head in half, making it easy to peel. Put the garlic, which is very soft, in a blender cup, add the chopped chili pepper without seeds, and a bit of warm water from the total amount. Start blending, then add salt. Add the remaining water and blend with the oil in a thin stream. If it's too liquid, add half a teaspoon of cornstarch and thicken slightly over low heat (it should be a very fluid cream, not thick!).

Cook the linguine, while placing the sauce in the pan where you'll later toss the pasta. Two or three minutes before the pasta is done, transfer it to the pan, which you have heated in the meantime. Mix well with the sauce and continue cooking, adding cooking water. Finish cooking, add a drizzle of oil, and toss. The result should not be dry, but a sort of very fluid cream created by the pasta starch.