In a large bowl, stir together flour, water, yeast, and 2 tsp. salt to make a shaggy dough. Turn out onto a clean, dry surface, dusting with any leftover flour from the bowl. Knead dough vigorously for 5 minutes, and shape into a ball. Arrange in a large, oiled bowl, cover with plastic wrap and a towel, and set aside in a warm spot until doubled in size, 1-1 ½ hours.
Meanwhile, put vinegar into a small saucepan and bring to a boil over MEDIUM-HIGH heat. Reduce heat to MEDIUM and gently boil until reduced to about ½ cup to make a glaze, about 30 minutes. Stir in honey and ½ tsp. white pepper and set aside to let cool.
Preheat oven to 475°F. Uncover bowl and punch down dough to deflate it. Transfer to a large sheet tray and evenly stretch out the dough into a roughly 14-inch circle, dimpling the dough all over with your fingertips.
Bake until just cooked through, about 10 minutes. Preheat gas or charcoal grill to 400°F. Brush steak with oil and season all over with salt and white pepper to taste. Place steak on oiled grates and grill for approximately 5 minutes on one side, or until moisture starts to pool on the top and beef releases easily from grates with tongs. Flip once, grilling on the other side for approximately 5 minutes or until internal temperature reaches 135°F with meat thermometer inserted into the thickest part of the steak.
Transfer steak to a plate and let rest for 5-10 minutes before thinly slicing against the grain (if using store-bought pizza crust, start the crust here). Meanwhile, arrange baked pizza crust on the grill to lightly char on the surface, 1-2 minutes, returning it to the sheet tray when done.
Top pizza crust with Monterey Jack cheese and bake until melted and bubbly, about 5 minutes. Top with beef, arugula, blue cheese, Parmesan cheese, and red pepper flakes, and drizzle with some of the balsamic glaze (reserving remaining for another use). Cut and serve immediately.
