Add 1 15-ounce can chickpeas (with liquid) to bowl of food processor fitted with multi-purpose blade or "S" blade. Secure lid on food processor and pulse 1 to 2 minutes until chickpeas are completely puréed and creamy. Stop processor and scrape down sides of bowl as needed to ensure all chickpeas are puréed. Set food processor aside.
Place large, heavy-bottomed pot on stovetop over medium heat. When pot is warm, add 1 tablespoon olive oil, drizzling oil over entire bottom of pot. Continue heating pot until oil is hot and shimmery.
When oil is ready, add 4 cloves garlic and stir to incorporate. Sauté garlic approximately 1 minute or until fragrant, stirring as needed.
Transfer puréed chickpeas from food processor bowl to pot, then add remaining 1 15-ounce can chickpeas (drained), 1 large Yukon gold potato (peeled, diced), ½ teaspoon paprika, and 2 cups low-sodium vegetable broth. Stir to incorporate ingredients, scraping bottom of pot to loosen any garlic that may have stuck to surface.
Cover pot with lid and increase heat under pot to medium-high. Bring liquid to boil, then immediately reduce heat under pot to medium-low. Simmer soup over medium-low heat 25 minutes or until potatoes are fork-tender. Stir soup occasionally to prevent sticking or burning.
Once potatoes are soft, a salt freshly cracked black pepper, and 2 tablespoons fresh lemon juice. Stir well to fully incorporate ingredients, then taste soup and adjust salt, pepper, and lemon juice as needed.
When satisfied with flavor of soup, portion soup into serving bowls. Top soup with drizzle of olive oil and sprinkle of freshly cracked black pepper, and serve immediately with French baguette pieces if desired.