1) To make the pasta: Combine the flour, eggs, and salt in a food processor and pulse until a smooth dough forms. Or mix with a hand or stand mixer; or by hand.
2) Knead the dough into a ball, wrap it in plastic, and set it aside to rest for 30 minutes.
3) For the tomatoes, heat a small, heavy-bottomed saucepan over low heat and add the oil. Once the oil is hot, add the garlic, and cook until it turns golden. Transfer the garlic to a paper towel to dry, reserving the oil.
4) Combine the tomatoes with the oil, garlic, and salt in a large bowl, tossing to combine. Set aside while you make the pasta.
5) Run the dough through a pasta machine on its thickest setting. Repeat the process, flouring as necessary, gradually reducing the thickness to the last setting. Cut along the length of pasta at foot-long intervals, then cut each into 3/4"-wide strands.
6) Bring 4 quarts water + 1 tablespoon salt to a boil. Drop the pasta into the boiling water, stir, then cook for 4 minutes.
7) Drain the pasta, and refresh under cold running water to stop the cooking. Continue to drain the pasta in a colander for 10 minutes or so, then toss with the tomatoes and fresh basil.
8) Serve immediately; or refrigerate and serve later.
Yield: 3 to 4 servings.