FOR THE MUSHROOMS:

1. In a large skillet, melt butter over medium-high heat.
2. Add shallot and mushrooms to the butter and give the mixture a good stir.
3. Stir brown sugar, salt, pepper, and the thyme leaves to the mushroom mixture. Stir to combine and cook until mushrooms and shallots have caramelized, about 5 minutes.
4. Remove cooked mushroom mixture from heat and set aside.

FOR THE FLATBREAD:

1. Pour balsamic vinegar into a small skillet and heat over medium-high heat until it reduces to a thick syrup, about 8 minutes. While the balsamic vinegar reduces, make the flatbread.
2. Heat a cast iron grill pan on the stove over medium-high heat. If you don't have a grill pan, you can use a real, outdoor grill (lucky you!) or just bake the flatbread in the oven at 500 degrees like you would a regular pizza.
3. Roll the pizza dough out to about 1/4 inch thick. Depending on the size of your pan, you may have to make flatbreads in batches.
4. Press dough onto hot grill pan. I like to use tongs to press the corners down so that I don't burn my fingers. Let dough cook for 2-3 minutes, until you can easily pick it up with tongs and dough has dark, charred grill marks.
5. When the first side of the dough has cooked, flip the dough over so the uncooked side is facing the pan.
6. Drizzle olive oil over the top of the flatbread, and quickly top with the mushroom mixture and crumbled goat cheese.
7. Cook until the goat cheese has softened and the bottom of the flatbread has nice, charred grill marks, about 4 minutes.
8. Remove pizza from grill pan and place on a cutting board. Top with thyme leaves and a drizzle of balsamic glaze. Slice and serve immediately.