In a small mixing bowl, whisk together the flour and matcha powder. Pour onto a clean, dry surface and create a small well in the middle. Crack the eggs directly into the well, then whisk gently with a fork, slowly bringing in some flour from the sides. Once eggs are mostly incorporated, begin kneading the dough with your hands. Keep kneading and pressing with the palm of your hand until everything has come together. There will be some extra flour that doesn’t make it into the dough, but that’s okay. About halfway through your kneading, wipe off your workspace so there is no additional flour. The dough will be a bit tough, but that’s how it’s supposed to be!
Cut the dough in half and roll out with a rolling pin until it’s thin enough to pass through the widest setting on your roller. Pass the dough through at this setting a few times, folding in half a couple of times if there are any holes. Once your dough passes easily through the widest setting, go up to the next thinnest setting and pass through a few times again. Continue this process until both of your pieces of dough have gone through setting 4, which is the recommended thickness for fettucine on the KitchenAid pasta roller.
Once again cut each sheet of dough in half so that you’re not working with super-long pieces of dough. Take each new sheet and roll it up like you would a fruit roll-up or tortilla. Slice each roll in ¼ to ½ inch pieces (the width of fettucine) and then unroll and spread out on a clean, dry surface to dry.
While your pasta is drying, prepare the sauce and toppings. In a large saute pan (one that will be big enough to hold all of the pasta and the toppings), warm one tablespoon of olive oil over medium-high heat. Add the chopped prosciutto and cook until crispy. Turn off heat. In a small mixing bowl, combine crème fraiche, the other tablespoon of olive oil, lemon juice, heavy cream, salt and pepper using a whisk. Set aside.
Bring a large saucepan of salted water to a boil. Once boiling, slide in the dried pasta and immediately start stirring with a wooden spoon (this will help prevent it from sticking together.) Bring water back to a boil. The pasta will be done cooking 5-10 seconds after the water starts boiling again. Keep an eye on it, it cooks quickly! Drain pasta and add to pan with crispy prosciutto.
Add minced garlic to the pan with the pasta, and then add the whipped crème fraiche sauce. Stir to combine. Add a tablespoon of butter to thicken things up a bit.
Stir arugula into pasta right before serving. Enjoy!