Preheat the oven to 375°F (190°C).
Cut focaccia into cubes; toast lightly if very soft. Add to a large mixing bowl.
Heat olive oil in a skillet; cook hot Italian sausage until browned.
Add pepperoni and cook 2–3 minutes more until edges crisp. Transfer both to the bowl with bread.
In the same skillet, sauté onions and celery until softened, about 5–6 minutes.
Add garlic and cook 1 minute.
Stir in red peppers, sun-dried tomatoes, and pepperoncini. Add thyme, sage, oregano, salt, pepper, and optional red pepper flakes.
Add the vegetable mixture to the bread mixture and toss lightly.
Add mozzarella and gently combine.
Whisk warm chicken broth with beaten eggs; pour evenly over stuffing. Toss until everything is moistened (add a splash more broth if needed).
Transfer mixture to a greased 9×13 baking dish.
Cover with foil and bake 30 minutes.
Uncover and bake another 15–20 minutes until golden brown on top.
Let rest 5 minutes before serving.