Make a large fountain with the flour and sprinkle with the salt. Crack the eggs in the center. Break up the eggs using a small fork and being careful not to incorporate much flour yet.
Using your fingers slowly begin to pull in flour from central edges of the fountain and swirl it in with the eggs. Keep doing this until all flour is incorporated and you form a ball.
Knead the dough until the underside is smooth.
Let the dough rest under plastic wrap while you set up a pasta machine.
Break the dough up into small pieces and roll them through the pasta machine starting at 1 and going up through 5.
Cut your pasta into wide strips. Set aside
Heat the olive oil in a large frying pan and add two cloves of garlic thinly sliced. Be careful not to burn or fry the garlic. In the mean time, get a pot of salted water boiling and add olive oil as well to keep the fresh pasta from sticking.
Just before the garlic slices start to brown add the onion (finely chopped) and the other two cloves of garlic minced, again being careful not to fry or burn.
Just before the onions turn translucent add the wine and cook until the smell of alcohol is gone (about 2-3 minutes)
Add the stock and cook for another 3 minutes.
Then add the peas and cook on low-medium low heat. When the peas begin to change color either mash them with a fork or use an immersion blender arm/stick to partially puree the peas. Leave some of them in full form.
When the water starts to boil add the pasta and cook for 2-3 minutes.
Add salt, black pepper and mint to the pea sauce. Also add 3-4 tablespoons of the water the pasta cooks in to the sauce depending on how much the liquid has cooked down.
Transfer the pasta to the frying pan using a slotted spoon and finish cooking in the pan covering the pasta with the sauce.
In order to wilt the pea shoots, drain the pasta over a colander that has washed pea shoots in it.
Transfer pasta to a bowl and sprinkle with grated parmigiano. Stir in pea shoots.