Begin by caramelizing the onions. Slice the onions into 1/8-inch slices.
Place in a pan (cast iron is recommended) and add the butter and olive oil.
Cook on medium-high heat, stirring occasionally.
As the onions release their water and begin to caramelize, adjust the temperature to avoid burning them, but keep them cooking at a steady pace.
Continue to check on the onions about every five minutes or so, and stir and scrape the bottom of your plan to release all of the "bits" that build up on the bottom.
*You may choose to add a tablespoon or two of water to the onions toward the end of your cooking time to deglaze the pan.
When the onions become the consistency of jam and turn a dark blond color they are ready. The whole process takes about 45-60 minutes.
While the onions are caramelizing, place the thinly sliced potatoes on the par-baked pizza crusts and sprinkle the rosemary on top of the potatoes.
Once the onions are ready, place them onto the pizza and then top each pizza with the cheese (you could shred the cheese, or add in slices for a more rustic look).