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. Stir occasionally, cooking 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 to stop the cooking process.
Drain the carrot tops, wring out excess liquid, and spread them on a plate to dry while you do the remaining recipe prep.
Add all of the ingredients from garlic through walnuts (if using) to the food processor. Blend until a chunky paste forms with small bits of carrot tops. Depending on the size of your food processor, you may need to stop frequently to scrape down the sides. Add the olive oil a tablespoon at a time until combined. Season to taste with salt, pepper, and more lemon juice if desired.
To use as a pasta sauce, cook your pasta in salted water according to package directions. Reserve 1/2 cup of pasta cooking water, drain the pasta, and return it to the pot. Add the reserved cooking water and carrot top pesto, stir to combine, and cook over low heat until warmed. Serve right away.
Otherwise, 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