Make the crackers: Preheat the oven to 350 degrees F. Combine the asiago and cayenne in a small bowl. Dust the pizza dough lightly with flour, then run it through a pasta roller, adjusting the setting thinner each time and dusting with more flour as needed, until about 1/8 inch thick.
Lightly beat the egg and 1 tablespoon water in a bowl. Brush the dough with the egg wash and sprinkle liberally with the asiago-cayenne mixture. Using a pizza wheel, cut the dough crosswise into triangles. Place the dough triangles on a baking sheet and bake until golden, 10 to 12 minutes. Let cool on the baking sheet.
Meanwhile, make the dip: Place the garlic in a small baking dish and roast in the oven until very soft when squeezed, about 40 minutes; let cool 10 minutes. Cut the top off the garlic and squeeze the roasted cloves out of the skin.
Place the roasted garlic in a food processor, add the asiago and season with salt. With the motor running, drizzle in the olive oil. Drizzle in up to 1/4 cup water if the dip is too thick. Taste and make sure it is delicious; re-season if needed. Serve with the crackers.