1. In a small bowl, dissolve yeast in the warm water. Let stand until creamy, about 10 minutes.
2. While yeast is proofing, heat 2 tbsp oil in skillet over medium heat. Add sliced onions and let brown, stirring every so often, allowing them to caramelize slowly. Once caramelized, remove from heat until ready to use for the pizza.
3. In a large bowl, combine 2 cups bread flour, olive oil, salt, white sugar and the yeast mixture; stir well to combine. Beat well until a stiff dough has formed. Cover and rise until doubled in volume, about 30 minutes. Meanwhile, preheat oven to 350 degrees F (175 degrees C)
4. While dough is rising, place goat cheese, basil leaves, and thyme in a mini-chopper and pulse until the herbs are well-integrated and the cheese is flecked with green throughout.
5. Line a baking sheet with parchment paper or aluminum foil, and dust with cornmeal. If using a pizza stone, you can skip the paper/foil. To keep the dough from sticking to your hands, rub your hands with either more cornmeal or some flour, and separate the dough into 4-5 equally shaped sections, around 6 inches in diameter. Arrange on the baking sheet and put about a 1/4-cup dollop of goat cheese mixture on top of each dough section.
6. Spread the herbed goat cheese out to cover the top of each pizzetta, and layer the caramelized onions, sliced tomatoes, and sliced mushrooms over top. Drizzle olive oil and balsamic vinegar lightly over top each pizzetta, and bake for 20-25 minutes.
7. When pizzette are done, garnish with chopped basil and enjoy!
Credit: Food52 by totalnoms, 8/15/2011 – http://food52.com/recipes/13964-pizzette-with-herbed-goat-cheese-heirloom-cherry-tomatoes.