Cook mushrooms and shallots: In a large pan, heat a generous drizzle of oil over medium high heat. Add mushrooms and shallots. Cook for 5 min, tossing occasionally. Add sliced garlic and cook for another 3-4 min, until mushrooms are golden and glistening and shallots are tender. Season with salt and pepper.
Preheat grill to high heat. Brush with oil.
Stretch dough balls into 2 pizza-shaped disks. Round, square or rustic all work! Transfer to a couple of lightly floured baking sheets.
Carefully transfer dough disks directly to the greased grill. Close the lid and cook for 2-4 min, until grill marks form on the bottom.
With a pair of tongs, flip pizza dough and cook the other side for another 2-4 min, until grill marks form. Use tongs to remove dough from grill.
Add par-cooked dough back to the baking sheet. Brush top of pizza dough with olive oil. Top with mozzarella, mushroom and shallot mixture. Crumble over gorgonzola. Sprinkle over thyme leaves.
Slide pizza directly onto grill, close the grill and cook for 3-5 min, until the cheese is melted and the crust is cooked to your liking. Transfer with tongs back onto the baking sheet for easy removal.
Serve pizza with cracked black pepper, flaky sea salt and chli flakes over to taste.