Remove prepared pizza dough from the refrigerator and place on counter for 30 minutes before using. Place pizza stone in cold oven with oven rack in bottom position. Turn heat to 450 degrees and allow stone to heat for at least a half hour before placing dough on stone.
Place a large pan on medium/high heat. Add 1-2 tablespoons olive oil to pan. When hot, add onions. Cook, stirring frequently until the onions are really going, then turn heat to medium and keep it there as onions reduce. When onions lose at least half their volume sprinkle with sea salt and pepper to taste. When onions are done (usually 25-30 minutes) turn off heat
Pizza prep: Cover pizza paddle with a thin layer of corn meal. Rollout one dough ball to make a 8-9 inch pie. Place rolled out dough on paddle. Brush dough lightly with olive oil and sprinkle with a layer of Parmesan cheese. Place 4-6 slices of prosciutto on top of cheese. Place half of caramelized onions on top of prosciutto and sprinkle with desired amount of goat cheese. Toss a handful of pine nuts on top. Then sprinkle with chives.
Use the paddle to place dough on preheated pizza stone and bake for 8-9 minutes. (To transfer dough onto stone: place tip of paddle an ich or so from the back edge of pizza stone, then use a slightly jerky back and forth motion with the paddle, the dough should slide right onto stone)
Remove pizza from oven, allow to rest for one minute then drizzle with desired amount of balsamic glaze (I suggest lots!). Slice and serve. Repeat on second pizza.