Heat 2 tablespoons extra virgin olive oil in a wide pot over medium-low heat. Add the leeks and season with a pinch of salt and pepper. Cook for 7 to 8 minutes, stirring often, until the leeks soften. Be careful not to brown them too much; adjust the heat to low as needed.
Cook the cherry tomatoes:
Add the cherry tomatoes to the pot and season with salt, pepper, and crushed red pepper. Sauté over medium heat with the leeks until the skins begin to split, about 5 minutes.
Simmer the sauce:
Add the white wine and bring to a boil. Reduce the heat to low and simmer the tomatoes and leeks, uncovered, for 25 to 30 minutes. Gently break the tomatoes apart as they simmer. Add a splash of water if the liquid in the pot evaporates too quickly. Taste and add more salt, pepper, or crushed red pepper if needed.
Cook the tagliatelle:
As the sauce simmers, cook the tagliatelle. Bring a large pot of generously salted water to a boil. Add the pasta and cook according to package directions. Scoop out ½ cup of the pasta cooking water and set it aside. Drain the pasta.
Finish the sauce:
Turn the heat on the sauce to medium. Once it begins to bubble, add the Parmesan cheese and basil. Stir until the cheese melts. Taste and season.
Blend the sauce (optional):
If you’d like a smoother sauce, use an immersion blender to purée the sauce to a smooth consistency. If using a traditional blender, be sure to return the sauce to the pot.
Finish the pasta:
Turn the heat on the sauce to medium. Add half the pasta cooking water and the cooked tagliatelle. Toss to coat for 1 to 2 minutes, adding more pasta water as needed, until the tagliatelle is completely coated. Turn off the heat.
To serve:
Transfer the pasta to a large serving bowl. Finish with more Parmesan cheese and fresh basil leaves on top. Enjoy!