Salt and pepper chicken. Heat a large skillet to medium-high and add olive oil, then sear the chicken, about 5 minutes a side. Make sure you get a nice sear on the chicken to add depth to the sauce. There should be lots of browned bits in stuck to the skillet. Move chicken to a plate and cover with tinfoil.
In the same pan, saute garlic in cooking spray for 30 seconds. Add mushrooms, thyme, a pinch of salt. Brown mushrooms, then deglaze pan white wine. Scrape the bits from the bottom of the pan and cook until wine is evaporated and mushrooms are soft, about 5 minutes
Whisk half and half, almond milk, and cornstarch together in a separate bowl. Add to the pan, bring to a low boil, then simmer until slightly thickened, about 5 minutes.
Add parmesan and stir until melted into the sauce. Place chicken and juices back in the skillet and simmer until chicken is heated through.