Step 1 Heat a 2-quart, deep, heavy-bottomed pan over medium-low heat. Add the grapeseed oil and onion and cook, stirring occasionally, until the onion begins to wilt and soften, about 10 minutes. Continue cooking until the onion slowly begins to collapse and caramelize, stirring more frequently. Cook until the onion is almost jam-like in consistency and is a rich golden-brown, 30 to 45 minutes. Remove the caramelized onions. You will need 4 teaspoons caramelized onions for the remainder of this recipe; the rest can be used in other recipes and will keep, covered and refrigerated, up to 1 week.
Step 2 In a small saucepan over medium-low heat, simmer the balsamic vinegar until it reduces almost by half to a syrup consistency (you should have about 3 teaspoons).
Step 3If you have one, place a pizza stone on the center rack of the oven and heat it to the highest setting possible (500 to 550 degrees). If you are using a wood-burning oven, heat it up.
Step 4Heat a large pan over medium-high heat until hot and melt the butter. In a single layer and with enough room between each, quickly sear the figs, cut-side down; this may need to be done in batches. Sear quickly enough that the figs are colored but not cooked or mushy. Set the figs aside to cool.
Step 5Stretch out the pizza dough to your desired size, thin enough in the center but leaving a rim around the edge. (At the restaurant, they stretch a 6-ounce dough ball into a 9-inch pizza disk.)
Step 6Sprinkle the dough with the olive oil and minced garlic, and drizzle over the reduced balsamic vinegar. Sprinkle the red onion, lardons, caramelized onions and blue cheese over the dough. Place the fig slices around the pizza, preferably cut-side up, and sprinkle over the Grana Padano. Season with a pinch each salt and pepper, or to taste.
Step 7Bake the flatbread directly on the stone or in a pan, baking until the crust is risen and browned, 5 to 7 minutes, depending on the setup of the oven and its heat. Be careful not to overbake the flatbread or it will dry out.
Step 8Cut the flatbread as desired, and drape slices of prosciutto over, then scatter over the arugula leaves. Garnish with the roasted grape clusters.