When oil is hot, reduce heat to Medium-High and add chicken. Cook until the internal temperature reaches 165 degrees (about 12 minutes), turning occasionally to keep from burning. Transfer to a plate and keep warm.
Wipe the pan clean of oil.
Add shallots and cook over Medium-High heat until translucent, about 3 minutes.
Add wine to deglaze pan, stirring with a spoon to scrape the bottom of pan, and cook until liquid is reduced by two-thirds.
Add heavy cream, demi-glace, cheese, red peppers, salt and pepper.
Stir until cheese is incorporated and sauce is thick enough to coat the back of a spoon.