In a small bowl, combine the active dry yeast, granulated sugar, and warm water. Stir gently and let sit for 5 to 10 minutes until foamy.
In a large mixing bowl, combine the bread flour and kosher salt. Add the yeast mixture and 1 tablespoon of olive oil. Stir until a shaggy dough forms.
Turn the dough onto a lightly floured surface and knead for about 8 minutes until smooth and elastic. Alternatively, use a stand mixer with a dough hook for 5 minutes.
Lightly oil a clean bowl with 1 tablespoon olive oil. Place the dough in the bowl, turning to coat with oil. Cover with a clean kitchen towel or plastic wrap and let rise in a warm place for 1 to 1.5 hours, until doubled in size.
While the dough is rising, melt the butter in a skillet over medium heat. Add the sliced onions, smoked paprika, and black pepper. Cook, stirring occasionally, until the onions are caramelized and soft, about 10 minutes. Remove from heat and set aside.
Preheat your oven to 500°F (260°C). Lightly oil a 10×14-inch Detroit-style pizza pan or a similar rectangular metal pan.
Once the dough has doubled, transfer it to the prepared pan. Using your fingers, gently stretch and press the dough to fill the pan evenly. If it resists, let it rest for 5 minutes and continue stretching until it reaches the edges.
Spread half of the barbecue sauce evenly over the dough.
Distribute the shredded chicken evenly over the sauce.
Sprinkle the shredded mozzarella and smoked gouda cheeses evenly over the chicken.
Scatter the caramelized onions over the cheese layer.
Drizzle the remaining barbecue sauce over the top in thin lines.
Bake the pizza in the preheated oven for 20 to 25 minutes, or until the crust is golden brown and crispy on the edges and the cheese is bubbly and slightly browned.
Remove the pizza from the oven and let it cool for 5 minutes before slicing into squares.
Serve warm and enjoy your Detroit Style BBQ Chicken Pizza!