Using a vegetable peeler (preferably a Y-style peeler), remove the zest from the lemons in long strips; try to remove only the colored portion of the peel, not the white pith just underneath. You should have about ⅔ cup zest strips.

In a large pot over medium-low, toast the almonds, stirring, until golden brown, about 5 minutes. Transfer to a small plate. In the same pot, bring 3 quarts water to a boil. Stir in the pasta and 2 teaspoons salt, then cook, stirring occasionally, until just shy of al dente.

Stir in half of the zest strips and cook until the pasta is al dente. Remove the pot from heat. Using tongs, transfer the zest strips to a food processor. Reserve 1 cup of the cooking water, then drain the pasta and return it to the pot.

To the food processor, add the remaining zest strips, ¾ cup of the almonds, the Parmesan and ¼ teaspoon each salt and pepper. Process until the mixture resembles coarse sand, 10 to 20 seconds.

Add the oil and process until incorporated (the mixture will not be smooth), about 10 seconds. Add the pesto to the pasta, along with the spinach and reserved pasta water; toss to combine. Taste and season with salt and pepper. Serve drizzled with additional oil and sprinkled with chives and the remaining almonds; serve additional Parmesan on the side.