Do some prep: Peel and thinly slice 6 to 7 ounces shallots. You should have 1 ½ cups sliced shallots. The goal is to slice them as evenly as possible (thickness-wise) so that they brown at a uniform rate. Remove the peel from 3 lemons in long strips with a vegetable peeler. Dice as finely as possible (you should have ⅓ cup) and add to a small bowl. Set aside. Finely chop 6 ounces pistachios.

Crisp aromatics: Have a medium strainer set over a medium bowl at the ready. To a medium pot or skillet (preferably not nonstick, which isn’t as effective as stainless, which allows you to see browning more clearly), combine 1 ½ cups olive oil, ¾ cup vegetable oil, 3 tablespoons fennel seeds, 2 tablespoons red pepper flakes, 1 ½ tablespoons sugar, 1 ½ tablespoons Diamond Crystal Kosher salt, and the sliced shallots. Bring to an active simmer over medium-high heat. Cook, stirring occasionally with a spoon and reducing heat as necessary to maintain a lively but gentle bubble, until shallots turn uniformly crisp and medium golden all over. This whole process will take somewhere between 15-20 minutes from the time when the oil begins to bubble, depending on the strength of your flame. If the shallots begin to take on color after a few minutes, turn down the heat– don’t rush it! As soon as the shallots are nearly ready, you will feel the mixture change in consistency: the shallots and seeds will begin to stick to each other, and you’ll be able to hear them as you stir them in the skillet– this means that they have lost their moisture and are crisping. (Realize that the shallots will continue to darken a bit even when they come off the heat, so be vigilant about stopping cooking as soon as they are golden.) Strain the entire mixture through the sieve over the bowl, shaking to remove any excess oil.

Crisp pistachios and finish oil: Return the strained oil to the pan, along with the chopped pistachios. Place the strainer with the shallots and aromatics back over the same bowl as before, and add the chopped lemon zest to the bowl (not the strainer!), so that when you strain the oil again in the next step, the zest will be kissed quickly with the hot oil. Turn the heat to medium. Cook the pistachios, stirring, until pistachios are lightly golden, about 2-5 minutes, depending on whether you are using raw or roasted pistachios. Strain nuts through the strainer (yep, right over the shallots) over the bowl with the lemon zest, shaking to remove as much oil from the strainer as possible. The lemon zest will sizzle! Let nuts and shallots cool completely in the strainer (over another bowl if necessary, so that they don’t sit in the strained oil), and then combine with the lemon zest-oil mixture and 1 ½ ounces coarsely grated Parmigiano Reggiano. Season to taste with flaky salt.