Heat 1 tablespoon of olive oil in a large skillet over medium-high heat.
Add the sliced bell peppers and sliced onion, season with salt and pepper, and sauté until tender, about 3–5 minutes, stirring occasionally.
Add the minced garlic and cook for 1 minute, then transfer the vegetables to a plate and set aside, keeping any accumulated juices.
Add the remaining 1 tablespoon olive oil to the skillet and heat until hot.
Add the thinly sliced chicken, Italian seasoning, smoked paprika, onion powder, oregano, salt, and pepper; spread the chicken into a single layer.
Let the chicken cook undisturbed for a couple minutes to brown, then stir and continue cooking until mostly cooked through, about 4–6 minutes total.
Stir in the soy sauce and cook until the chicken is fully cooked through and no longer pink, about 1–2 more minutes.
Return the cooked peppers and onions and any juices to the skillet, stir to combine, and spread the mixture evenly.
Sprinkle the shredded provolone evenly over the chicken and vegetables, cover the skillet, and cook 1–2 minutes until the cheese melts.
Serve immediately and garnish with chopped green onions if desired.