Season both sides of the chicken well with salt and pepper.
Heat the oil in a non-stick pan over medium heat. Once the oil is hot, sear the chicken on both sides to a deep golden brown. Remove the chicken and transfer to a plate.
In the same pan, melt the butter and saute the spinach until wilted, stir in the flour. Cook for about 1 minute until the roux starts to turn golden brown. Slowly stir in the broth and milk and bring to a simmer. Add the chicken to the pan and cook to an internal temperature of 160 degrees using a thermometer. Then remove from heat.
Stir in parmesan cheese. Taste and adjust the seasoning as needed with salt and pepper.
Serve with bread.
Notes
Pro tips: Butterfly the chicken: Lay the breasts down on a cutting board, using a sharp knife parallel to the cutting board slice the breasts through the middle (carefully) all the way in half.