Rip the bread into large pieces and put them into a bowl. Add water to cover, then pull out the bread quickly and squeeze out the excess water, leaving squishy soaked bread.
Place the bread in a food processor or blender, and add the pimentos, lemon juice, garlic, paprika, cayenne, and salt. Process until well blended. Add the olive oil in a very thin steady stream, using the insert made for this purpose or just doing it by hand. As the oil gets incorporated, the mixture should emulsify (thicken).
Scrape the mixture into a bowl.
Notes
One thing I love about my blender and food processor is that the top has an opening that allows you to pour the oil into it very slowly while the rouille is blending up and emulsifying. In some cases there is even a tiny hole in the top which allows you to add the oil at once, and then the hole drips in the oil at a very steady and slow pace all on its own. Anyone who has ever tried to follow a recipe that says “drizzle in the olive oil very slowly while whisking” knows this is a great invention.