Heat the olive oil and butter in a large skillet or cast iron pan over medium heat.
Add the onions, separating them as you add them to the skillet. Toss the onions to coat with the oil and butter. Add the salt.
Cook over medium heat, stirring occasionally for about 8-10 minutes.
Reduce heat to medium low and cook for another 20-25 minutes until the onions are a darker golden brown.
Add 2-3 tablespoons of water or broth to deglaze the pan, scraping up all of the brown bits.
For ready-to-use flatbread, spread with a layer of fig jam. Spread the caramelized onions on top and finish with the goat cheese. See note about using raw dough.
Bake the flatbread for 7-8 minutes or until heated through. Turn on the broiler and cook for an additional minute. Garnish with fresh rosemary before serving.
Notes
I used 2 squares of the O'Doughs gluten free flatbread for this recipe, but any flatbread will work. If using pizza dough be sure to prepare the dough according to package directions before adding toppings.