Season both sides of the chicken cutlets with salt, black pepper, and dried oregano.
Heat olive oil in a 12-inch heavy-bottomed skillet over medium-high heat until shimmering.
Place chicken in the skillet and sear for 5 to 6 minutes per side until the internal temperature reaches 165 degrees Fahrenheit.
Remove chicken from the skillet and transfer to a warm plate.
Add the diced onion to the remaining fat in the skillet and sauté for 3 minutes until translucent.
Incorporate the minced garlic and cook for 60 seconds until fragrant.
Pour in the chicken broth to deglaze the pan, scraping the bottom with a wooden spoon to release browned bits.
Add the fresh spinach in batches, tossing with tongs until completely wilted, approximately 2 to 3 minutes.
Stir in the lemon juice and return the chicken to the pan to reheat for 1 minute.
Garnish with grated Parmesan cheese and serve immediately.