Divide flour into two medium bowls (3/4 cup in each). In one bowl, add 2 egg yolks and 1 whole egg.
Combine eggs with flour until a dough begins to form. Transfer to a clean work surface and knead for 8-10 minutes, until elastic and cohesive. Wrap dough and place in fridge to chill.
Mix basil in a high-powered blender with 2 egg whites until fully combined. Add to the second bowl of flour and once again mix into a dough.
Place green dough on counter and knead for 8-10 minutes until elastic and cohesive. Wrap dough and place in fridge to chill with the other dough for at least 30 minutes.
When the doughs are rested, remove one from the fridge and prepare a pasta roller. Cut dough in half and coat in flour.
Roll dough through the pasta machine from setting 1 to 6, ending with a long, rectangular sheet of pasta dough. Flour the sheet generously with flour and roll into a log.
Cut pasta log into 4 equal wide sections, unfurling the past strands into long noodles. Coat in flour and wrap in a nest until ready to cook. Repeat process with rest of pasta doughs.
Peel outer layers of hard skin from the zucchini and squash and cut into thin ribbons with a potato peeler or mandolin. Set aside and cover.
Heat a large pot with about 6 quarts of water until boiling. Add a large pinch of table salt and cook 1/4 of your pasta at a time (using both green and yellow noodles) for 1 minute.
Meanwhile, heat a sauté pan over medium heat. Melt 4 tbsp unsalted butter and add 2 tbsp olive oil, 2 cloves of chopped fresh garlic, and sauté as the pasta cooks.
Just before adding the pasta, add 1/4 of your zucchini and squash ribbons. Then, add your cooked pasta, the juice of 1/2 lemon, and 1/4 cup grated parmesan.
Shake the pan to coat pasta in the sauce and transfer to a large plate. Garnish with extra olive oil, flaky sea salt, and fresh cracked black pepper.