Bring vinegar to a boil in a small nonreactive saucepan and cook, stirring occasionally, until reduced to 1/2 cup. Stir in the honey and season with salt and pepper, to taste.
For the steak:
Heat grill to high. Brush steak on both sides with oil and season with salt and pepper. Grill until golden brown and slightly charred on both sides and cooked to medium-rare doneness, about 5 minutes per side. Remove from the grill to a cutting board, tent lightly with foil and let rest for 10 minutes. Slice into 1/4-inch thick slices.
For the pizza:
Heat the grill to high.
Brush both sides of the pizzas with oil and season with salt and pepper. Grill until golden brown on both sides, about 2 minutes per side. Remove from the grill, divide the Monterey Jack cheese over the top of each one and then sprinkle with the blue cheese. Place back on the grill, close the cover of the grill and grill until the cheese has melted, about 1 minute. Remove to a flat surface, divide the steak between each pizza, then top with the watercress Drizzle with some of the balsamic glaze and sprinkle with some of the shaved Parmigiano-Reggiano.
In a large bowl stir together 1/3 cup water, yeast, and sugar and let stand until foamy, about 10 minutes. Stir in remaining 1/3 cup water, 2 tablespoons oil, 1 3/4 cups flour, cornmeal, and salt and blend until the mixture forms a dough. Knead dough on a floured surface, incorporating as much of remaining 1/4 cup flour, as necessary, to prevent dough from sticking, until smooth about 5 to 10 minutes. Form the dough into a ball.
Lightly oil the sides and bottom of a large bowl with oil, add the dough, turn to coat in the oil, cover and let rise in a warm place until doubled in size, about 1 hour. Gently punch the dough down and divide into 4 equal pieces. Roll each piece on a lightly floured surface into a 10-inch circle that is 1/8-inch thick. Brush off excess flour and transfer the dough to a baking sheet, cover each circle of dough with plastic wrap and continue stacking rolled out pieces on top of each other. Wrap well with plastic wrap and refrigerate until ready to grill.