In a medium bowl, combine yeast with 1/2 c warm water. Let stand until foamy, about 5 minutes. Add sugar and 3/4 c flour. Stir well and let stand until very foamy, about 30 minutes.
In bowl of a stand mixer, combine remaining 2 c flour with shredded cheese, nuts and salt. With paddle attachment, add sponge from first step along with remaining 6 tbsp water and the butter. Work until a dough is formed. Change to dough hook and knead until smooth, about 3 minutes.
Line a baking sheet with parchment paper or Silpat. Divide dough into 3 pieces, forming each into a log about 12" long and 3" wide. Place logs on baking sheet about 2" apart. Cover with lightly damp paper towel, then with plastic wrap. Let stand 45 min until risen.
Meanwhile, preheat oven to 350°F Remove the plastic wrap and paper towel, and dust logs with Parmesan cheese. Bake about 35 min, until golden, puffed, and interior temperature is 205°F Let cool on baking sheet for 20 minutes.
Lower oven temp to 300°F Position 2 racks in lower third and upper third of oven. Transfer logs to cutting board; cut on the bias into 2/3" slices with a serrated knife. Place slices, cut side up, on 2 baking sheets. Bake 45-60 min until golden and crisp. Turn biscotti over halfway through; at the same time, swap sheets upper for lower, and rotate each sheet 180°. When done, transfer to a rack to cool.