Let pizza dough sit at room temperature for at least an hour. Slice onions and then put olive oil and butter in a large fry pan and heat until melted. Stir in onions over medium heat and sauté over low heat for about 25 minutes. When onions are tender and balsamic and brown sugar, stirring over low heat until blended. Set aside. These may be done ahead, stored in fridge or frozen!
Preheat oven to 400 degrees. On a lightly floured surface roll dough into a rectangle, making sure it is not a perfect rectangle, of course. Line a baking sheet with foil and scatter a bit of cornmeal on it. Transfer flatbread dough onto your prepared sheet and begin by adding your caramelized onions, sliced pears, and gorgonzola on top of flatbread dough. Put in oven and bake for about 20 minutes or until cheese is bubbly and it looks incredible. Place arugula on top of flatbread, gently pressing it into the flatbread. Remove, cut into pieces and serve. Serves 6 to 8.
In a large fry pan add oil and butter and heat to medium. Add sliced mushrooms and onion and sauté for about 5 minutes and then add fresh thyme leaves. Continue to cook until mushrooms are tender. Season to taste with salt and pepper. Set aside to cool.
Prepare dough the same way as the other flatbread, laying it on a prepared baking sheet with cornmeal scattered on top. Scatter cooked mushrooms and onion on top of flatbread and then dot with crumbled goat cheese. Bake for about 18 minutes and remove from oven when flatbread looks golden. Cut into pieces. Serves 6 to 8. *You may also add some lemon zest on top of cheese before baking, if you like.