In a large mixing bowl, combine flour and salt. Create a well in the center and add eggs and olive oil. Whisk the eggs and incorporate the flour until a rough dough forms. Knead for 8-10 minutes until smooth and elastic.

Wrap the dough in plastic wrap and let it rest for at least 30 minutes at room temperature.

Divide the rested dough into quarters and roll each piece into thin sheets, dusting with flour to prevent sticking.

In a skillet, heat olive oil and sauté minced garlic until fragrant. Add cherry tomatoes and cook for 5-7 minutes. Stir in basil leaves and season with salt and pepper.

Boil salted water and add the fresh pasta. Cook for 2-4 minutes until it floats to the top. Drain, reserving some pasta water.

Combine the drained pasta with the sauce in the skillet, tossing gently. Adjust sauce consistency with reserved pasta water if necessary. Cook for an additional minute.

Serve immediately, garnished with grated Parmesan and fresh basil leaves.