Slice each chicken breast in half long ways so each piece becomes two thinner pieces.
Pour flour into a small bowl.
Season chicken breasts with salt and pepper and dredge in flour.
Heat skillet to medium high and coat with a tablespoon of olive oil.
In batches, cook the chicken breast pieces for 2 minutes on each side or until cooked through and nicely browned on the outside. Add more oil to the pan as needed with each batch until all chicken is cooked.
While chicken is cooking finely chop onions and wash mushrooms.
Once all chicken is cooked, set aside.
Keeping the heat at medium-high, put another tablespoon of oil in the now empty skillet and add onions and mushrooms and cook until soft but not brown, around 6-10 minutes. Reduce heat if needed.
Once onions and mushrooms are soft pour in marsala and deglaze the pan by bringing the wine to to a boil. Stirring occasionally, cook until most of the liquid is evaporated, about 2-5 minutes.
While that is happening you can prepare chicken stock whisked together with the cornstarch. Once most of the wine has evaporated from the step above, add the chicken stock mixture and cook another 2 minutes until sauce begins to thicken up.
Reduce heat to medium- low, add tablespoon of non-dairy butter and fresh thyme. Stir to mix.
Add chicken back in, coat with mushroom sauce, and cook for 2-3 minutes to reheat chicken.
If sauce becomes too thick as it cools, it can be thinned out with water or more chicken stock when reheating.