To blanch the carrot tops: remove thick stem pieces. Bring a pot of water to a boil. Prepare a large bowl with ice cubes and cold water in it. Once boiling, add the carrot tops to the pot. Cook for about 3 minutes or until bright green and tender. Immediately remove from the pot, drain the hot water, and add the carrot tops to the ice cube bowl.
Drain the carrot tops and spread them on a plate to dry while you do the remaining recipe prep.
Add all of the ingredients except oil to the food processor. Blend until a chunky paste forms with small bits of carrot tops. Add the olive oil a tablespoon at a time until combined. Season to taste with salt, pepper, and more lemon juice if desired.
Once cooled to room temperature, store the pesto in the fridge in an airtight container for several days. The bright green color may fade to a slightly darker green, and this is totally normal.