Heat 3 tablespoons oil in large pot over medium heat. Add onion; cook until translucent, about 8 minutes. Add chorizo and paprika; stir 1 minute.
Add potatoes and broth. Increase heat and bring to boil. Add kale; stir until wilted and soup returns to boil. Reduce heat to low, cover, and simmer 1 hour, stirring occasionally.
Meanwhile, heat 2 tablespoons oil in large skillet over medium heat. Add bread cubes and sauté until golden, about 10 minutes. Sprinkle croutons with salt and pepper.
Divide soup among bowls. Top with croutons and serve.
Note: Soup and croutons can be made separately ahead of time.