Season the chicken strips evenly with salt and pepper. Heat olive oil and butter in a large skillet over medium-high heat. Add the chicken and chopped onion, cooking until the chicken is lightly browned and the onion softens, about 7 to 8 minutes.
Stir in the minced garlic and cook briefly until fragrant. Pour in the chicken broth and bring it to a boil. Add the quick-cook brown rice, stir well, cover the skillet, and lower the heat. Let it simmer for about 5 minutes so the rice begins absorbing the liquid.
Uncover the skillet and add the spinach in batches, allowing it to wilt before adding more. Once all the spinach is added, cover the pan and remove it from heat. Let it rest for about 5 minutes so the rice finishes cooking and the flavors blend.
Stir everything gently to combine. Sprinkle freshly grated Parmesan cheese over the dish and let it melt naturally. Serve immediately while warm.