Make flat bread according to linked recipe directions. Set aside.
Make Veggies: Heat olive oil in large sauté pan over medium heat. Add mushrooms, onions, pepper, salt, and garlic powder. Stir to combine. Cook until browned and caramelized (about 20-30 min.), stirring occasionally. Towards end of cooking, you may need to add a small amount of water (1 tablespoon or so) occasionally to deglaze the pan and keep from burning. You want browning. Remove from heat and set aside.
While veggies are cooking, make Sauce: In small saucepan over medium-low heat, melt ghee. Add garlic and cook 30 sec., stirring constantly. Add white wine and cook 1 min. Add milk, salt, Dijon mustard, and dried thyme. Whisk together and continue whisking for 4-5 minutes to thicken slightly. Add spelt and whisk 1 more minute. Remove from heat, cover, and set aside.
Preheat oven to 425℉. Place flatbreads on two baking racks set on baking trays. Divide sauce evenly among the flatbreads, spreading into a thin layer on each. Top with veggies, brie slices, chopped pecans, and thyme. Bake 10-15 minutes until brie is melted and toppings are hot. After removing flatbreads from oven, top with fresh thyme sprigs, if desired.