Mix flour with salt and pour it onto a clean counter surface. Make a small well in the center of the flour and crack in your eggs and egg yolks.
Use a fork to scramble eggs and slowly incorporate flour into the egg mixture.
After a few minutes, the egg mixture should be pretty thick and you can start to lightly fold it over itself and knead in more flour. Keep kneading in more flour until the dough is firm and not sticky, about 10 minutes of kneading. You won’t need all the flour most likely.
When the dough is smooth and firm and not sticky at all, it’s done. Wrap it in plastic wrap at this point and let it rest at room temperature for an hour. You can also freeze it at this point for longer storage.
To make the pasta, cut the dough into thirds or quarters and work with one piece at a time. Flour the dough well and start running it through your pasta machine on the widest setting. Do this a few times, folding and turning the dough to knead it a bit more.
Once the dough is in a smooth sheet, start cranking down the pasta machine. Roll the dough through each setting making sure it stays nicely floured so it doesn’t stick. Stop on the second to thinnest setting. Then run it through the angel hair cutter to cut the pasta into shape.
Toss pasta with flour and set aside as you do the other pieces of dough.
To make primavera:
Chop broccoli, asparagus, and green beans into large pieces. Blanch in heavily salted water for 60-90 seconds. You can use the same water to cook the pasta later.
Remove veggies from water with a slotted spoon and rinse with cold water to stop the cooking.
In a large high-walled pan or skillet, add olive oil, crushed garlic, and red pepper flakes over low heat. Cook for a few minutes to let the garlic flavors infuse into the oil. Be careful not to burn the garlic.
Turn heat up to medium and add the zucchini, red pepper slices, and scallions. Cook for another minute or two.
Add blanched veggies to the pan along with stock, cream, and parmesan.
Add pasta to boiling water to cook. The pasta should take only a minute or two to cook assuming you are using angel hair.
When pasta is done, transfer straight to pan with veggies. Toss to coat the pasta with the sauce and mix with veggies.
Serve immediately with chopped basil and extra Parmesan.