Add the oil and butter to the skillet, allowing the butter to melt.
Add the chicken to the pan. Cook the first side 2-3 minutes before flipping. Cook the second side 2-3 minutes. You want it lightly golden.
Remove the chicken from the pan and add the shallots and mushrooms. Allow them to sauté until the shallots are tender and fragrant and the mushrooms are beginning to brown.
Add the Marsala to the pan, making sure to scrape up any brown bits on the bottom of the pan.
Add the heavy cream and Dijon. Stir to combine.
Add the chicken back to the pan along with any drippings. Allow the sauce to simmer and thicken.