For the dip: Preheat the oven to 350 degrees F. Place the garlic bulbs in the oven and roast until soft when squeezed, about 30 minutes; let cool for 10 minutes. Cut the tops off the garlic and squeeze the roasted cloves out of the skin.
Place the roasted garlic in a food processor with the cheese and season with salt. With the machine running drizzle in the olive oil. Taste and make sure it is delicious; re-season if needed.
For the crackers: In a small bowl combine the Asiago and cayenne.
Run the Calzone Dough through a pasta roller, adjusting the setting thinner until the dough gets very thin, about 1/8-inch thick. Dust the dough lightly with flour during the process if the dough is sticky.
Brush the dough with the egg wash and sprinkle liberally with the Asiago-cayenne mix. Using a pizza wheel, cut the dough crosswise into triangles. Place the dough triangles onto a sheet tray and bake until light brown, 10 to 12 minutes. Let cool for 3 to 4 minutes on the tray before removing.
Eat right away or store in an airtight container.
In a small bowl, combine the yeast and sugar and whisk together with the warm water. Let sit for 15 minutes; when the water looks frothy and smells very yeasty, it's ready.
In the bowl of a standing mixer fitted with the dough hook attachment, add the flours and salt. Pour in the yeast-water mixture and the olive oil. Mix to combine on medium speed. When a dough ball has formed, continue to knead until the dough is tight and not at all sticky, 5 to 6 minutes.
Lightly oil a mixing bowl, place the dough in the bowl and cover with a tea towel or plastic wrap. Place the bowl in a warm place to let rise until doubled in size, about 1 hour. Punch the dough down and let it rise a final time for 30 to 40 minutes before using.