Heat 1 tablespoon olive oil in a large skillet over medium-high heat.
Add the sliced mushrooms and cook about 2 minutes, stirring occasionally, until they begin to soften.
Add the minced garlic and cook, stirring, about 1 minute until fragrant.
Meanwhile, season the chicken strips with 1 teaspoon salt, 1/2 teaspoon black pepper, 1/2 teaspoon dried oregano, and a pinch of red pepper flakes.
Push the mushrooms to the edges of the skillet and place the seasoned chicken in the center in a single layer.
Cook the chicken 3–4 minutes on the first side until golden, then flip and cook another 3–4 minutes on the other side.
Pour 1 cup pizza sauce over the chicken, cover the skillet, and cook until the chicken is almost cooked through, about 3–5 minutes.
Sprinkle 1 1/2 cups mozzarella evenly over the chicken, then add pepperoni and sliced olives (or other toppings) to taste.
Cover and cook until the cheese is melted and the chicken is cooked through (internal temperature 165°F), about 2–4 more minutes.
Serve the skillet pizza chicken hot with desired sides.