Heat olive oil in a large pot over medium-high heat and cook onion until soft and translucent, about 5 minutes. Add garlic and cook until fragrant, about 1 minute. Add cauliflower and potato. Combine water and tomato paste in a jar and pour into the pot. Cook on medium-low heat until cauliflower and potato are soft, about 15 minutes.
Stir chickpeas into the pot. Season with mint, salt, and pepper and heat until hot, 2 to 3 minutes.