Heat your Blackstone to medium-high heat. In a large sauté pan, add the butter, sliced leeks, garlic, fresh thyme, and sliced button mushrooms. Season with a pinch of salt and pepper. Cook for 5-6 minutes, stirring often.
In a small mixing bowl, whisk together the flour and milk until smooth. Add the milk mixture to the sauté pan and stir to combine. If needed, adjust the sauce’s thickness with a little water or extra milk. Cook for another 5 minutes, stirring occasionally.
On the griddle, melt the butter and add the sliced king oyster, maitake, and shiitake mushrooms. Cook for 3-4 minutes per side, until golden and slightly crispy.
Toast the flatbreads on the griddle, starting with the presentation side for 2-3 minutes, then flip to toast the bottom.
Spoon the mushroom sauce evenly onto the flatbread, then top with the caramelized mushrooms. Garnish with chopped parsley and Grana Padano. Slice and serve.
