Prepare Chickpeas and Vegetables: Drain and rinse the canned chickpeas. Peel and cube the potato. Roughly chop the onion, garlic (4 cloves), green bell pepper, and carrot.
Sauté Vegetables: Heat 3 tablespoons (45 ml) of extra virgin olive oil in a large frying pan or stock pot over medium heat. Add the chopped onion, garlic (4 cloves), bell pepper, and carrot. Continuously stir and sauté for about 4 minutes until lightly softened.
Add Vinegar and Spices: Add 1 tablespoon (15 ml) red wine vinegar, 1 teaspoon sweet smoked Spanish paprika, and 1 teaspoon dried oregano to the sautéed vegetables. Mix well to make the ingredients aromatic.
Add Potato and Chickpeas: Add the cubed potato and drained chickpeas to the pan. Season generously with sea salt and freshly cracked black pepper. Gently mix to combine.
Add Liquid and Simmer: Pour in 2 1/2 cups (600 ml) of water (or broth if preferred). Increase heat to high and bring to a boil. Once boiling, cover with a lid, reduce heat to low-medium, and simmer for 15 to 20 minutes until potatoes are tender.
Prepare Garlic and Egg Mixture: In a separate frying pan, heat 2 tablespoons (30 ml) extra virgin olive oil over medium heat. Add 3 whole peeled garlic cloves and crack in 1 egg (crack into a bowl first to avoid shells). Fry until garlic is lightly browned and egg is fully cooked.
Make Paste: Remove garlic and egg from heat and transfer to a mortar. Add 2 tablespoons (8 g) chopped parsley and a pinch of sea salt. Pound with a pestle until a paste-like texture forms. Alternatively, use a food processor or finely chop on a cutting board.
Combine and Serve: Remove lid from chickpea mixture. Add the garlic and egg paste to the pan and gently mix until well combined. Remove from heat and serve warm, ideally with crunchy baguette and Spanish red wine.