Step 1
Warmth ⅓ cup vegetable oil in a big Dutch oven or different heavy pot over medium-high. Cook dinner one fourth of 2 giant leeks, white and pale inexperienced components solely, thinly sliced, stirring often, till deep golden brown and crisp, 6–8 minutes. Drain via a fine-mesh sieve set over a small bowl; instantly season with kosher salt and toss to mix. Set crispy leeks apart. Reserve pot.
Step 2
Warmth 1 Tbsp. leek oil in reserved pot over medium-high (reserve remaining oil for utilizing in salad dressings, sauces, or roasting greens). Cook dinner 1 lemon, halved, seeds eliminated, minimize aspect down, till deeply browned, 2–3 minutes. Switch to a plate.
Step 3
Scale back warmth to medium; soften 2 Tbsp. unsalted butter in pot. Add remaining leeks, season with salt, and cook dinner, stirring often, till softened however with out having taken on a lot shade, about 5 minutes.
Step 4
Return lemon to pot and add 1 Parmesan rind (if utilizing), 6 cups low-sodium vegetable broth, and a few grinds of freshly floor pepper; season with salt. Enhance warmth to excessive and convey broth to a boil. Scale back warmth to medium; simmer till decreased barely and broth smells lemony, about quarter-hour.
Step 5
Utilizing tongs, fish out lemon halves, squeezing gently so as to add some juice to pot, and discard. Take away Parmesan rind and discard. Add one 1.1-lb. bundle shelf-stable or refrigerated gnocchi to pot and simmer till cooked via, about 5 minutes. Take away from warmth, add 2 (packed) cups torn Tuscan kale leaves, and stir till simply wilted.
Step 6
Ladle soup into bowls and high with torn dill sprigs, shaved Parmesan, and reserved crispy leeks; season with extra pepper.
