Place bacon in a large pot and cook over medium heat, turning occasionally, until evenly browned, about 10 minutes. Drain bacon pieces on paper towels.
Heat olive oil over medium heat in the same pot. Add onion, garlic, and thyme; cook and stir until onion is softened, about 10 minutes. Stir in wine; cook until slightly reduced, about 4 minutes. Add chicken broth, black-eyed peas, and cauliflower florets. Season with black pepper. Bring to a boil. Reduce heat, cover, and simmer soup until flavors combine, about 20 minutes.
Remove soup from heat and let cool briefly, about 10 minutes. Puree soup with an immersion blender until smooth. Top with bacon pieces.