Heat olive oil in a large stockpot over medium-low heat. Add minced garlic and smoked paprika and cook, stirring, until fragrant, 1 to 2 minutes. Add vegetable stock, black-eyed peas, and bay leaves and bring to a boil. Once boiling, cover and reduce heat to medium-low. Simmer until beans are just tender, about 30 minutes.
Add kale and simmer 10 additional minutes. Add red pepper flakes, lemon juice, and 1 ounce of cheese. Taste and season with salt and pepper as needed. Remove and discard bay leaves and keep soup warm over low heat.
Meanwhile, make the croutons. Heat broiler and halve remaining garlic clove. Rub bread slices with garlic clove and broil directly on oven rack until just toasted, 2 to 3 minutes. Remove from oven, place on a parchment-lined baking sheet, top with equal portions of grated cheese, then return to the oven for an additional 2 to 3 minutes to melt the cheese.
Once croutons are done, ladle soup into bowls and top each bowl with a crouton. Serve.