Heat 2 tablespoons oil in a small Dutch oven over medium-high heat. Add chopped carrots, chopped onion and ¼ teaspoon salt; cook, stirring occasionally, until slightly softened, about 6 minutes.
Add chopped kale, chopped garlic and ½ teaspoon crushed red pepper; cook, stirring often, until the kale is wilted, about 2 minutes.
Add 1½ cups broth; cook, stirring occasionally, until slightly reduced, about 5 minutes.
Stir in the remaining 1½ cups broth and ½ teaspoon salt. Continue cooking until the kale is tender, about 5 minutes.
Meanwhile, place half of the rinsed beans in a small bowl; using a fork, mash until mostly smooth.
Stir the mashed beans and the remaining whole beans into the stew. Bring to a lively simmer over medium-high heat. Simmer, stirring occasionally, until the broth thickens slightly, about 4 minutes.
Stir in 2 tablespoons lemon juice. Remove from heat.
In a small bowl, combine ¼ cup Parmesan, 2 tablespoons parsley and 1 teaspoon lemon zest.
Divide the stew among 4 shallow bowls. Top each serving with the Parmesan mixture and drizzle with the remaining 4 teaspoons oil (1 teaspoon per bowl).
