Marinate the chicken in the buttermilk in the refrigerator overnight.
Make the demi-glace. Heat the olive-oil in a heavy saucepan. Add celery, carrots, and onion. Cook on medium-high heat, stirring frequently, for about 10 minutes.
Add red wine and cook until reduced by half.
Add beef broth and tomato paste and stir well. Decrease heat to medium and simmer for about 20 to 25 minutes. Mixture should be reduced by 1/4. (Can be made a few days in advance and refrigerated.)
To make gravy, cook mushrooms and onion in 2 tablespoons olive oil in a heavy saucepan until onion is translucent, about 7 minutes. Add demi-glace and salt and simmer for about 20 minutes. Season with pepper and keep warm.
To fry chicken, heat canola oil in a cast iron pan over medium heat to 325 degrees.
In a pie plate, combine flour, cornstarch, salt and pepper.
Drain the chicken and dredge in flour mixture. Fry in oil for 4 to 5 minutes per side or until cooked through.