Heat the olive oil in a large skillet over medium heat. Add the chopped onion and cook for 3 to 4 minutes, stirring occasionally, until softened. Stir in the minced garlic and red pepper flakes, if using, and cook for another 30 to 60 seconds until fragrant.
Add the drained white beans, vegetable broth, dried thyme, salt, and black pepper. Stir gently to combine, then bring the mixture to a gentle simmer. Cook for 4 to 5 minutes, allowing the beans to warm through and absorb some of the savory broth.
Pour in the heavy cream and stir until evenly incorporated. Use the back of a spoon to gently mash a few of the beans against the side of the skillet. This releases their starch and helps thicken the sauce without requiring extra flour. Simmer for 3 to 4 minutes.
Add the chopped kale to the skillet in batches if needed. Stir until the leaves begin to wilt, then cook for another 3 to 5 minutes, until tender but still vibrant green. If the sauce becomes too thick, add a small splash of vegetable broth.
Remove the skillet from the heat and stir in the grated Parmesan cheese and fresh lemon juice. Taste and adjust the salt, pepper, or lemon juice as needed. Let the beans rest for a minute or two so the sauce can settle into a creamy consistency.
Sprinkle with chopped fresh parsley and a little extra Parmesan, if desired. Serve warm with crusty bread, toasted sourdough, or a simple green salad.