1 pound all-purpose flour, plus more as needed
½ teaspoon fine sea salt, plus more for the pasta water
5 large eggs
1 tablespoon extra-virgin olive oil
¼ cup extra-virgin olive oil
2 cloves garlic, very thinly sliced
¾ pound (about 1 pint) cherry tomatoes, halved
Salt and freshly ground black pepper
18 fresh basil leaves, cut into ⅓-inch thick slices
About 1 cup finely grated Parmesan, plus more for serving
1. Make the pasta: Place the flour on a work surface and shape it into a mound. Sprinkle with salt and make a wide well in the center. Add the eggs and oil to the well and beat them with your fingers or a fork until combined. Gradually pull small amounts of flour from the inside walls of the well into the egg mixture and mix until a stiff dough forms. Knead the dough, adding more flour if needed to prevent it from sticking. Let the dough rest, covered with a damp cloth, for 30 minutes.
2. Cut the dough into thirds, shape into a circle, and flatten each piece with your hands. On a floured surface, roll the dough until very thin, about 1 mm, flipping it over as you roll and flouring as needed. Fold the pasta round in half from top to bottom and then fold in half again from top to bottom. Cut the rectangle crosswise into ¼-inch-thick ribbons. Unroll the ribbons and toss with flour. Spread on a floured parchment sheet and let dry for 30 minutes.
3. Bring a large pot of salted water to a boil. It should taste salty like the ocean.
4. Prepare the sauce: Heat the oil in a large skillet over medium-high heat. Add the garlic and sauté, without coloring, until just fragrant, about 30 seconds. Immediately add the tomatoes; season generously with salt and pepper and sauté to extract some of the juices and soften the tomatoes. Remove from the heat until the pasta is cooked.
5. Add half of the pasta to the boiling salted water (refrigerate the other half to use later) and cook until al dente, about 4 minutes.
6. Pull the pasta from the pot and drop it directly into the sauce. Set the sauce over medium heat and add a little pasta cooking liquid to loosen it. Stir in the basil, Parmesan and more pasta cooking liquid to create a saucy consistency. Serve with more grated Parmesan.