Bring a medium pot of water to a boil. Add the cilantro and blanch for 10 seconds. Remove and shock in an ice bath. Pat dry well on paper towels, squeezing to remove any excess water. Roughly chop and transfer to a blender. With the machine running, add the oil, salt, and cayenne and process until smooth. Transfer to a bowl, cover, and refrigerate overnight. Strain through a fine mesh strainer, pressing against the solids with the back of a spoon to extract as much oil as possible. Transfer to a squirt bottle and refrigerate until needed, for up to 2 weeks. (Bring to room temperature before using.)