Heat 1 tablespoon olive oil in a large skillet over medium-high heat.
Season chicken with salt and pepper, cook until browned and cooked through, about 6 to 8 minutes.
Remove chicken and set aside.
Add remaining olive oil to the skillet and cook chopped onion for 2 to 3 minutes until softened.
Add garlic and mushrooms; cook 4 to 5 minutes until mushrooms release moisture and start to brown.
Stir in orzo to coat with vegetables and oil.
Pour in chicken broth and add oregano or Italian seasoning; bring to a gentle simmer.
Reduce heat to medium-low, cover, and cook for 10 to 12 minutes until orzo is tender and most liquid is absorbed.
Stir cooked chicken and fresh spinach into the orzo until the spinach wilts.
Mix in Parmesan cheese and adjust seasoning with salt, pepper, and optional red pepper flakes.
Serve warm with extra Parmesan and optional fresh lemon juice or zest.