Bring a large kettle of water to a rolling boil.

Submerge fennel fronds and cook for 1 minute. Drain and immediately stop cooking by running under cold water.

Squeeze out excess water, transfer to a clean dish towel, and squeeze dry.

Place in a blender with 1/4 cup oil. Blend, adding additional oil, if needed, to make a slurry.

Transfer to a non-reactive container and refrigerate overnight.

Line a funnel with a piece of butter muslin and strain out oil. Discard fennel fronds.