Salt the short ribs on all sides and place them on the counter for 20 minutes. If you can, salt them and place them in the fridge overnight.
Heat an oven safe pan or pot on medium-high with olive oil. Before adding the short ribs, season with black pepper. Add the Short ribs bone side down first and sear on both sides. Meanwhile, heat the oven to 275.
While the Short Ribs are searing, Cut the top of a whole head of garlic and place it cut side down on the pan along with the herbs and whole peppercorns.
Cover then pan and transfer to the oven. Cook for 2-3 hours rotating them halfway and uncovering them at the last 30 minutes (before uncovering them, make sure they're already tender).
Remove from the oven, place them on a plate and shred.
Remove the garlic bulbs from the roasted head and place them in a small bowl, smash them until you get a paste (add a little bit of the oil from the short rib pan to help it spread on the pizza)
Place the pan with the fat/oil on the stove on medium-high heat. Add the mushrooms and cook for about 3 minutes, stirring constantly. Remove from the pan and place them in a paper-towel-lined plate.
Next, do the same with the shallot slices. Cook them in the oil until translucent and almost crispy. Place them in a paper-towel-lined plate as well.
Pre-heat your oven to 500 degrees. Roll out your dough on a lightly floured surface into a large circle (or rectangle) Spread the garlic paste onto the dough, Next add the chopped/shredded short ribs, then the mushrooms, then the cheese and shallots. Place on a baking sheet or pizza stone and bake for about 15 minutes, or until the dough is golden brown and the cheese is bubbly.