Place 1 garlic clove, smashed, and ½ large bunch kale, ribs and stems removed, leaves coarsely chopped, in a blender and top with 2 cups boiling water. Blend until smooth; set purée aside.

Heat 3 Tbsp. extra-virgin olive oil in a medium heavy pot over medium-high. Add 1 medium onion, coarsely chopped, and season with kosher salt. Cook, stirring occasionally, until softened, about 4 minutes. Add 3 garlic cloves, thinly sliced, and ½ tsp. crushed red pepper flakes; season with freshly ground black pepper. Cook, stirring often, until fragrant, about 1 minute. Add 4 cups low-sodium vegetable broth, 1½ tsp. Diamond Crystal or 1 tsp. Morton kosher salt, and 3 cups water and bring to a boil. Add 12 oz. whole wheat pasta and cook, stirring occasionally, until very al dente, about 2 minutes less than package directions. Add two 15.5-oz. cans white beans, rinsed, 2 oz. Parmesan, finely grated, and remaining ½ large bunch kale, ribs and stems removed, leaves coarsely chopped. Reduce heat to medium and cook, stirring occasionally, until kale is tender and beans are heated through, about 2 minutes. Pour in reserved purée and cook, stirring occasionally, until combined but color is still vibrant, about 1 minute. Remove from heat and stir in 3 Tbsp. fresh lemon juice.

Ladle soup into bowls; drizzle with plain whole-milk yogurt and season with black pepper.