Slice 4 large white onions to desired thickness. Using a wide bottomed skillet, add enough olive oil where it coats the entire pan and cook on medium/high heat. When the oil begins to shimmer, add onions and stir to fully coat all the onions with oil. Cook 10 minutes stirring occasionally. Add salt and sugar; bring the heat down to medium/low. Cook an additional 30–40 minutes, stirring occasionally, until your onions are completely caramelized. If your onions begin to dry out during this process add more olive oil or a little water. Set aside.
Preheat your grill or oven to 400 degrees.
On a flat, floured surface roll out the pizza dough making 6 small flat breads, about a 1/4-inch thick. Brush each side of the dough with olive oil and grill flatbreads on a pizza stone or bake in oven until just barely cooked, pull off and let cool 5 minutes.
Once cooled, rub half a garlic clove over each side of the flatbread and brush with olive oil. Add mushrooms, caramelized onions, and blue cheese. Grill or bake each flatbread until cheese is melted, top with fresh arugula, and enjoy!