Set a large soup pot or Dutch oven over medium heat and add the olive oil.

Add the chopped onion and carrot to the pot. Cook for 6 to 8 minutes, stirring a few times, until the vegetables are softened and the onion looks translucent.

Add the chopped garlic to the pot. Stir for about 30 seconds, just until the garlic smells fragrant.

Add the tomato paste to the pot. Stir it into the vegetables and cook for 1 minute, until it darkens slightly.

Sprinkle the cumin and paprika into the pot. Stir for about 20 seconds so the spices bloom in the hot oil and tomato paste.

Add the red lentils, chickpeas, vegetable broth, and water to the pot. Stir well to combine.

Raise the heat to medium-high and bring the soup to a boil.

Add the kosher salt and black pepper to the pot and stir again.

Lower the heat to medium-low so the soup stays at a gentle simmer. Leave the pot partly covered and cook for 18 to 22 minutes, stirring once or twice, until the lentils are very soft and starting to break apart.

Stir the soup well. Use the back of a wooden spoon or a potato masher to crush some of the lentils and a few chickpeas against the side of the pot, which will make the soup a little thicker without turning it fully smooth.

Taste the soup. Add more salt or black pepper if needed, and add a small splash of water if the soup feels thicker than you want.

Put the butter and dried mint in a small skillet or small saucepan over medium-low heat. Cook for 1 to 2 minutes, swirling the pan once or twice, until the butter is melted and the mint smells warm and toasty.