Prep the greens: Trim the carrot greens from the stems. Keep the tender leaves and thinner stems; discard tough, woody stems. Wash thoroughly to remove grit, then spin or pat dry.

Toast the nuts: Warm a small skillet over medium heat. Add your nuts or seeds and toast, shaking the pan, until fragrant and lightly golden, 3–5 minutes. Let cool. This step boosts flavor and helps the pesto taste nutty, not flat.

Start the base: In a food processor, add carrot greens, parsley (if using), garlic, lemon zest, 1 tablespoon lemon juice, toasted nuts, and a big pinch of salt and pepper. Pulse until finely chopped.

Stream in oil: With the machine running, drizzle in 1/2 cup olive oil until the mixture loosens into a spoonable sauce. Scrape down the sides and pulse again. Add more oil if you prefer a looser texture.

Add cheese: Pulse in the Parmesan or Pecorino until just combined. Taste and adjust salt, lemon juice, and pepper. If you like heat, add a pinch of red pepper flakes.

Check consistency: For pasta, aim for a saucy texture that clings. For spreading, keep it slightly thicker. If it’s bitter, add another teaspoon of lemon juice or a pinch of sugar to round it out.

Serve: Spoon over warm pasta with a splash of reserved pasta water, dollop on grilled chicken or fish, spread on toast with ricotta, or swirl into soup. It also makes a bright dressing when thinned with more oil and lemon.