Rinse the lentils thoroughly in a fine mesh strainer and be sure to pick out any tiny stones or debris. Set aside. If you're serving with croutons, preheat the oven to 400°F.

Pour the olive oil into a Dutch oven or other heavy-bottomed pot and set on medium-low heat. Stir in the garlic, celery, onion, fennel, chili pepper, thyme sprigs, and bay leaf. Cook until the vegetables are softened and their perfume starts to fill the kitchen, about 7 minutes. Season with the salt.

Add the potatoes and stir to coat them with oil. Add 1 cup of broth and turn the heat to medium. Bring the mixture to a simmer over medium heat, then cover partly and cook until the potatoes have started to soften, about 10 minutes. Stir in the rinsed lentils.

Pour in the remaining 3 cups broth, plus the 4 cups water. Use a wooden spoon or silicone spatula to mash some of the softened potatoes against the side of the pot; this will help to thicken the soup. Turn the heat to high to bring the soup to a boil, then lower the heat to simmer and cover partially. Simmer gently for 45 minutes, or until the vegetables are tender and the lentils are cooked through.

While the soup is simmering, toss the bread cubes in a bowl with 2 tablespoons olive oil, sprinkle with salt and pepper, and spread them out on a baking sheet. Bake in the hot oven until evenly browned and crisp, about 15 minutes.

Remove the soup from the heat. Discard the thyme sprigs, bay leaf, chili pepper, and any garlic cloves that haven’t melted into the soup—or leave them in, as I do (I like to mash them up). Ladle the soup into bowls, drizzle with your best olive oil, and scatter a small handful of croutons on top of each serving.