While the pizza dough is rising, caramelize the onions and fennel*. Heat the olive oil (1/4 to 1/2 cup depending on your skillet’s size) in a large heavy-bottomed sauté pan over medium-high heat. Once the oil is shimmering, add the onions and fennel and stir to coat.
Keep stirring occasionally for 10 minutes. Add salt and continue to cook for 30 more minutes to an hour, stirring every couple of minutes. You want the onions and fennel to start sticking a little to the pan and getting brown but you’ll want to stir enough that they don’t burn.
If the onions and fennel are getting really dry or are close to burning you can add a little water to the pan or more olive oil (you can also use broth, wine, or bourbon).
Keep going until the onions and fennel are a rich brown color. Taste and add more salt if needed. Set aside.*
In a food processor, pulse the goat cheese, 1 tablespoon olive oil, lemon juice, black pepper, and Chinese five-spice blend until smooth and well blended. Set aside.
Adjust the oven rack to the upper-middle position and preheat the oven to 500 degrees Fahrenheit. Use a pastry brush to grease a 12-inch oven-safe skillet with 2 tablespoons olive oil. It will seem like a lot but you want the oil to fry the bottom of the pizza crust, making it nice and crispy.
Transfer the pizza dough to a lightly floured surface and divide it in half. Cover the half you aren’t rolling out with lightly greased plastic wrap. Press and roll the other piece of dough out into an 11-inch circle, trying to keep the dough thickness even throughout.
Transfer the dough to the prepared skillet and reshape if necessary.
Use a pastry brush to lightly spread extra-virgin olive oil over crust and sprinkle with kosher salt.
Very lightly* spread some of the cheese mixture over the crust (about 2 to 3 tablespoons).
Top with caramelized onions and fennel.
Add 8 to 9 teaspoon-sized dollops of the cheese mixture on top of the caramelized onions and fennel and spread them out slightly.
Drizzle balsamic vinegar over the pizza (about 1 tablespoon) and sprinkle the grated pecorino romano cheese on top.
Sprinkle fennel fronds on top of everything.
Put the skillet over high heat and cook until the edge of the dough is set, the pizza is slightly puffed, and the bottom of the crust looks spotty brown (3 minutes).
Transfer to the oven and bake for 7 to 10 minutes until the edges are brown
Remove the skillet and slide the pizza onto a wire rack and let cool slightly.
Repeat steps 6-17 for the second pizza. Or freeze the dough to save for later (see notes).