Add all of the ingredients except for the olive oil to a food processor. Pulse 5 to 10 times, or until the ingredients are roughly chopped.: The first pulses release aromas as the beet greens , shelled pistachios , and roasted garlic break down. You will notice an immediate green fragrance with nutty undertones, and the mixture should look coarsely chopped, not a puree. This texture stage matters because it determines how much structure remains in the final pesto. Too many pulses here can make the nuts turn past coarse into a paste, so stop while you still see distinct bits. A common mistake is over-processing, which can heat the mixture and dull the fresh color, so pulse in short bursts and scrape the bowl if needed.
Turn the food processor on and slowly stream the olive oil through the opening at the top.: As you drizzle the olive oil , the mixture will begin to shine and coalesce, transforming from dusty bits into a glossy, cohesive pesto. Listen for a steady motor hum and watch for the mixture to smooth out, with the oil binding tiny flecks of green and nutty pearls. Pouring too quickly can cause the oil to separate instead of emulsify, leaving a greasy top layer. If separation occurs, stop adding oil and pulse briefly to bring it back together. The ideal cue is a velvety texture that holds together on a spoon.
Taste the pesto for flavor and add more sea salt, vinegar, or garlic to taste.: This is when the flavors harmonize, and you must fine tune. I sample a small spoonful to check salt, acidity, and garlic presence. The cider vinegar should lift the overall profile without tasting vinegary, and the sea salt should make the green notes pop. If the pesto feels heavy, another splash of vinegar lifts it. One common pitfall is over-salting before tasting with the intended accompaniment, so season cautiously.
Use immediately or transfer to a sealable container and refrigerate until ready to use. Pesto will stay fresh for up to 7 days in a sealed container in the refrigerator.: Fresh pesto has bright color and lively aroma right away, and when stored it mellows but remains flavorful. Press a thin layer of olive oil on top before sealing to slow oxidation and color loss. You will notice aroma fade over days, which is normal, but the taste remains vibrant. Avoid leaving it at room temperature for long periods, as that shortens its shelf life. A typical error is storing without oil seal, which leads to faster browning and flavor degradation.