Prep the leeks: Cut off the roots and the top few inches of dark green tops first, then thinly slice the remaining leeks. Add to a bowl of cold water and gently agitate them to loosen the dirt. Use your hands or a slotted spoon to scoop out the leeks onto a clean towel and pat dry (don’t drain them, or the dirt will fall back into the leeks).
Make the Bouquet Garni: Gather the bay leaves, sage sprigs, and thyme sprigs in a single pile. Use kitchen twine to tightly tie them together (see Note 1). Set aside.
Heat the 2 tablespoons of olive oil in a Dutch oven or soup pot over medium-high heat. Once shimmering, add the leeks with a few pinches of salt. Cook until softened and starting to brown, 7 to 9 minutes, stirring occasionally.a. While this cooks, rinse the potatoes, then peel and dice them. Add the garlic and chili flakes to the pot. Cook for 1 to 2 minutes, stirring frequently. If needed, add a splash of broth to deglaze, scraping up any browned bits. Add the broth, Bouquet Garni, ½ teaspoon kosher salt, pepper to taste, potatoes, and beans. Stir well.
Bring the soup to a boil. Then reduce the heat to medium-low, cover the pot, and simmer the soup for 20 to 25 minutes, or until the potatoes are tender, uncovering to stir a few times.
Meanwhile, make the Herby Oil: Finely chop the parsley and dill. Using a microplane, zest the lemons on top of the parsley, then grate the garlic into the mix. Add to a small jar (this makes it easier to distribute the oil). NOTE: If you prefer things less lemony, start with 1 lemon's zest. Stir in the flaky sea salt and the ¼ cup (56g) olive oil. Taste, adding more salt to taste. Once the potatoes are tender, scoop out the Bouquet Garni and discard. Blend about half of the soup (3 to 3 ½ cups / 680 to 800g).a. Stand blender option: Transfer half of the soup to a stand blender. Replace the blender cap with a dish towel to allow the steam to vent. Blend until thick and smooth. Return to the pot and stir to incorporate.b. One-pot option: Use an immersion blender throughout half of the soup, but be sure to not blend it all—you want to retain some texture. Add the baby spinach to the soup. Simmer for 2 minutes, or until the spinach has wilted and is silky. Season to taste with salt and pepper.
Serve the soup in bowls. Spoon the Herby Oil over each bowl.