Combine flour and salt in a standing mixer fitted with a dough hook.
Add in the eggs, one at a time and continue to stir. (They should start to pull flour in from the sides into a well in the center.)
Stream in 1 T. olive oil.
When most of the dough starts to form a ball, remove from the mixer.
Knead on a floured surface for 10 minutes. It should become smooth and elastic.
Lightly coat with olive oil, wrap in plastic wrap, and let it rest for 30 minutes.
Roll out pasta with your pasta machine (or by hand) until the dough is thin enough to see light through. (On our pasta machine, I only went down to 2 instead of 1.)
Combine all filling ingredients together. Set aside.
Prepare your pasta with filling in whatever fashion you'd like – hand folding, molding, machine, whatever!
Drop pasta into boiling water for 3-5 minutes, or until cooked through.
Brown butter in a skillet, and flash fry sage in the butter.
Pour butter over pasta and serve!