Add the flour, egg, water, and olive oil to the bowl of a stand mixer fitted with the paddle attachment.
Mix on low speed until the ingredients begin to come together into a shaggy dough.
Switch to the dough hook and knead on low speed for 5-7 minutes, or until the dough is smooth, elastic, and no longer sticky.
Form the dough into a ball, wrap tightly in plastic wrap, and let it rest at room temperature for 30 minutes to 1 hour.
Cut the dough into two equal pieces and lightly flour each piece.
Using a KitchenAid pasta roller attachment, begin rolling the dough on the widest setting. Fold the dough in thirds, rotate it 90 degrees, and pass it through again. Repeat 2-3 times to develop a smooth sheet.
Gradually reduce the roller thickness one setting at a time until you reach your desired thickness.
Feed the pasta sheet through the spaghetti or fettuccine cutter attachment.
Lightly dust the pasta with flour to prevent sticking while you prepare the water.
Bring a large pot of generously salted water to a rolling boil.
Cook the fresh pasta for 1-2 minutes, or until tender with a slight bite.
Transfer directly to your favourite pasta sauce and toss until evenly coated.