Cook bacon in a Dutch oven over medium heat until crisp. Remove bacon from pan using a slotted spoon, and crumble.
Add 1 cup carrot and chopped onion to drippings in pan, and cook for 4 minutes, stirring occasionally. Add garlic, and cook for 1 minute, stirring constantly. Add paprika, 1/4 teaspoon salt, cumin, and red pepper; cook for 30 seconds, stirring constantly. Stir in chicken broth, 1 cup water, and beans; bring to a boil. Reduce heat, and simmer for 20 minutes, stirring occasionally.
Add 4 cups kale to bean mixture. Cover and simmer for 10 minutes or until kale is tender, stirring occasionally. Ladle about 1 1/4 cups bean mixture into each of 4 bowls, and top each serving with 2 tablespoons yogurt. Sprinkle with bacon, and serve with lemon wedges, if desired.