In a saucepan, melt the butter and caramelize the onions for 10 minutes. When the onions turn golden brown, add the honey and balsamic vinegar. Cook over low heat for 5 minutes.
Preheat the oven to 450°F (230°C).
On a floured work surface, roll out the pizza dough into a circle or rectangle. Place on a pizza stone or baking sheet.
Spread the BBQ sauce over the dough and evenly distribute the caramelized onions over the entire surface of the dough.
Add the chorizo slices, hot peppers, and mushrooms. Cover everything with cheese. Bake for 15 minutes.
