In a large pot or Dutch oven, heat olive oil over medium heat. Add onion and sauté until lightly golden, about 5 minutes.
Stir in garlic, celery, and carrots. Cook an additional 10 minutes, stirring occasionally, until the veggies are softened and slightly caramelized.
Deglaze the pot with white wine, allowing it to reduce and almost fully evaporate, approximately 5 minutes.
Add the cannellini beans, broth (starting with 2 1/2 cups), tomato paste, salt, pepper, red pepper flakes, Italian seasoning, thyme, oregano, and bay leaves. Stir well, bring to a boil, then reduce the heat to low and cover. Let it simmer for 15 minutes.
Remove and discard the bay leaves. Carefully transfer about 2 1/2–3 cups of the soup to a blender and puree until smooth.
Pour the blended mixture back into the pot and stir to combine. Adjust consistency by adding more broth if desired.
Add chopped kale and simmer for 3–5 minutes, or until the kale is wilted.
Taste and adjust seasonings as needed. A splash of lemon juice or an extra pinch of salt enhances the flavors.
Serve warm, garnished with fresh herbs if desired. Pair with crusty bread for a satisfying meal!