In a large mixing bowl, combine 2 cups of all-purpose flour and a pinch of salt. Create a well in the center and crack 3 large eggs into it. Using a fork, gently whisk the eggs, gradually incorporating the flour from the edges until the dough begins to come together. This should take about 5 minutes, and the mixture will look shaggy but cohesive.

Transfer the dough onto a lightly floured surface and knead it for about 8-10 minutes until it becomes smooth and elastic. You should notice a slight sheen on the dough's surface. If it feels sticky, sprinkle a bit more flour as needed. Once ready, shape the dough into a ball, cover it with a clean kitchen towel, and let it rest for 30 minutes to relax the gluten.

After resting, divide the dough into 4 equal pieces. Working with one piece at a time, flatten it slightly with your hands, then roll it out using a pasta machine or a rolling pin to your desired thickness, typically about 1/16 inch. Dust with flour to prevent sticking, and repeat with the remaining pieces. You can cut the rolled sheets into your preferred pasta shapes once they're thin enough.

Bring a large pot of salted water to a boil over medium-high heat. Gently add your freshly cut pasta into the boiling water and cook for 2-3 minutes until they float to the surface and are tender yet firm to the bite. Drain the pasta, reserving a bit of cooking water in case you need to adjust your sauce later.

While the pasta cooks, heat 1 cup of heavy cream over medium heat in a large skillet until it simmers. Add in 1/2 cup of freshly grated Parmesan cheese and stir until melted and well combined. Toss in minced garlic for added flavor, and let the sauce reduce slightly for about 2-3 minutes until it's creamy and thickened. If desired, stir in chopped fresh basil at the end for a beautiful aroma.

Once the pasta is cooked and drained, quickly add it to the skillet with the sauce. Toss everything together gently, allowing the pasta to soak up the flavors for about 1-2 minutes. If the sauce seems too thick, add a splash of reserved pasta water. Plate your deliciously easy homemade pasta, garnishing with additional Parmesan and fresh basil for a colorful finish that’s sure to impress!