4 tablespoons extra-virgin olive oil
1 head garlic, halved crosswise
10 ounces Parmesan rinds, enclosed in cheesecloth or muslin
1 lemon, rind peeled into thick strips with a vegetable peeler, then halved and juiced
8 sprigs fresh thyme
½ teaspoon red-pepper flakes
1 pound hearty greens (such as escarole, kale, mustard greens or rapini), stemmed and torn into bite-size pieces
Kosher salt and black pepper
2 (15-ounce) cans white beans (such as Great Northern or cannellini) or chickpeas, drained and rinsed
Freshly grated Parmesan, for serving

1. To make the Parmesan broth: In a large pot, heat 2 tablespoons olive oil over medium-high. Add the garlic, cut-sides down, and cook until golden brown, 2 to 3 minutes. Add the Parmesan rinds, lemon rinds, thyme and 8 cups water and bring to a boil. Reduce heat to a simmer and cook, uncovered, until the broth tastes full and rich and is reduced by half, 1 to 1 1/2 hours. (You will have about 4 cups of broth.) Reserve half the garlic and half the lemon rinds, then strain the broth. (Once cool, the broth will keep for 1 week refrigerated or 3 months in the freezer. If freezing, leave a bit of space between the broth and the lid of the container, as the broth will expand.)
2. To make the soup: Squeeze the garlic cloves to release them from the reserved head. Finely chop the reserved lemon rind. In a large pot, heat the remaining 2 tablespoons olive oil over medium-low. Add the garlic cloves and the red-pepper flakes and cook, breaking up the garlic with your spoon, just until fragrant, 2 to 3 minutes.
3. Increase the heat to medium, add the greens and the chopped lemon rind and a pinch each of salt and pepper. Cook, stirring, until the greens are wilted, 1 to 2 minutes.
4. Add the beans and all of the Parmesan broth and bring to a boil. Reduce the heat to a simmer, cover, and cook until the greens are silky and the beans and broth are warmed through, about 10 minutes.
5. Remove from heat and stir in the lemon juice to taste. Season to taste with salt and pepper. Serve with black pepper and grated Parmesan on top.

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