- 2½ cups (10 ounces) all-purpose flour, plus additional for kneading
- ½ teaspoon fine sea salt
- 1 large egg
- 1½ cups tepid water
- 4 tablespoons (¼ cup) unsalted butter or olive oil, or a combination
- 1 medium onion, diced
- 1 medium carrot, peeled and diced
- ½ teaspoon fine sea salt
- 2 garlic cloves, minced
- 3 medium ripe tomatoes, chopped, juices reserved, or one 15-ounce can tomatoes, chopped, with their juices
- 1 teaspoon Turkish or other crushed red pepper flakes, or to taste
- 1 heaping tablespoon dried purple basil (or substitute 1 tablespoon dried regular basil plus 1 teaspoon ground anise)
- 3 tablespoons tomato paste, mixed with ¼ cup warm water
- 1 small potato, peeled and diced (optional)
- 1 cup flat green or brown lentils, soaked overnight, or Le Puy lentils, unsoaked
- 2 tablespoons unsalted butter
- 2 tablespoons olive or vegetable oil
- Dried purple or regular basil, for serving (optional)
- Crushed red pepper flakes, for serving
Whisk the flour and salt together in a large bowl. Make a well in the center and break in the egg. Use your finger to break the yolk and to mix it with the white, then mix the flour and egg, turning the bowl as you pull the flour in from the sides and pressing the mixture together with the heel of your hand until it is relatively dry and crumbly. Add the water ¼ cup at a time, mixing the ingredients after each addition, until the dough is somewhat firm; a finger pressed into it should leave an imprint. Very lightly flour your work surface, turn the dough out, and knead until smooth, about 5 minutes, adding flour as necessary to keep the dough from sticking. Wrap the dough in plastic and refrigerate for at least 1 hour, and up to 24 hours.
Heat the butter and/or oil in a 5-quart pot or Dutch oven over medium heat. Add the onion, carrot, and salt and cook until the vegetables are softened, about 5 minutes. Add the garlic and stir for 1 minute. Add the tomatoes with their juices and cook, stirring, until they soften and break down almost to a paste, 8 to 10 minutes.
Add the red pepper flakes and stir until they color the other ingredients in the pot, about 2 minutes. Add the basil (or basil and anise) and stir once, then add the tomato paste mixture, the potato, if using, lentils, and hot water and bring to a boil. Lower the heat to a simmer and cook, partially covered, until the lentils are soft and the broth tastes rich and tomatoey, 30 minutes to 1 hour, depending on the variety of lentils (Le Puy lentils will cook more quickly). The soup should be thick but not so thick that it cannot accommodate the noodles; if necessary add water ¼ cup at a time to attain the correct consistency. Turn off the heat and cover to keep warm.
Remove the dough from the refrigerator. Cut off about one eighth of it; rewrap the rest and set aside. Roll the small piece of dough into a rope ¼ to ½ inch thick. Lay it on your work surface and press your fingers or the heels of your hands along its length, flattening it as you go. Cut into ½-inch pieces and set the croutons aside on a lightly oiled plate.
Unwrap the rest of the dough and divide it in half. On a lightly floured surface, use a rolling pin to flatten and stretch one of the pieces until it is about ⅛ inch thick. Don’t worry if the dough is of uneven thickness or an odd shape. To cut the noodles, place the side of your left hand about ½ inch in from the upper edge of the dough (vice versa if you are left-handed) and use it as a guide to cut noodles approximately ½ inch wide. Move your guiding hand across the dough, cutting as you go, until you’ve cut it all. Don’t worry if your noodles are uneven in size, some long and others short, some wider or narrower. Mound the noodles on your countertop or a plate, sprinkle lightly with flour, and toss. Repeat with the other piece of dough.
Bring the soup to a boil and add the noodles. Cook at a medium simmer, stirring occasionally to make sure that the noodles cook evenly, until they are tender but not mushy, about 15 minutes.
While the noodles are cooking, fry the croutons. Melt the butter with the oil in a small skillet over low heat. Add the croutons and cook, stirring and turning, until they crisp, puff up, and become golden; don’t let them brown. Remove to a paper towel to drain.
Serve the soup in wide bowls, scattered with the croutons. Pass dried basil, if you like, and red pepper flakes at the table.