Mix warm water, yeast, and sugar in a bowl. Let it sit for 5 minutes until foamy (this is crucial — if it doesn't foam, your yeast is dead). Add flour, olive oil, and salt, then stir until shaggy dough forms. Knead for about 8 minutes until smooth.
Place dough in an oiled bowl and cover with a damp towel. Let it rise at room temperature for 90 minutes or until doubled in size. Don't panic if your kitchen is cool — it just takes a bit longer, and honestly that's fine.
Preheat your oven to 425°F. While it heats, shred your cooked chicken breast and toss it with half the BBQ sauce in a small bowl. Taste and adjust — some BBQ sauces run sweeter than others.
Punch down the risen dough and divide it in half. Roll each half into a circle about 10 inches wide. Transfer to two pizza pans or baking sheets and poke the surface with your fingers to create dimples.
Spread the remaining BBQ sauce over each crust, leaving a half-inch border. Scatter the seasoned chicken evenly across both pizzas, then top with mozzarella cheese. Sprinkle minced garlic and oregano over the cheese.
Add diced red onion, black olives, and bell pepper on top. Bake for 12-15 minutes until the crust is golden and the cheese bubbles. Keep an eye on it after minute 10 — ovens vary wildly, and you want that cheese melted but not burned.
Let pizzas rest for 3-4 minutes before slicing. This prevents the cheese from sliding right off when you cut into it. Slice into 4 pieces per pizza and serve immediately while everything's hot.