Roll out the pasta to the thinnest setting and cut into 4-inch squares. Place 1 tablespoon potato mixture in the center of each square. Fold the opposite corners of each square together, press firmly to seal, and form a triangle. Bring the opposite points of the triangle together and press firmly to meld. Continue until all the pasta is stuffed and formed into tortelli. Drop the pasta into boiling water and cook until tender, about 6 to 7 minutes.
Meanwhile, melt the butter in a 12 to 14-inch saute pan and continue cooking until golden brown color appears in the thinnest liquid of the butter. Add the sage leaves and remove from heat. Add the lemon juice and set aside. Drain the tortelli well, gently pour them into the saute pan, and return to heat. Add the remaining 1/4 cup chives and 1/4 cup cheese, toss to coat and serve immediately.
As you expand the well, keep pushing the flour up from the base of the mound to retain the well shape. The dough will come together when half of the flour is incorporated.
Start kneading the dough with both hands, using the palms of your hands. Once you have a cohesive mass, remove the dough from the board, and scrape up and discard any leftover bits. Lightly re-flour the board and continue kneading for six more minutes. The dough should be elastic and a little sticky. Wrap the dough in plastic and allow to rest for 30 minutes at room temperature.