In a large bowl, whisk together honey, dijon mustard, mayonnaise, lemon juice, a pinch of salt, and a pinch of pepper. Remove about ½ cup of the honey mustard sauce from the bowl and reserve for later.
Pound out any fatter areas of the chicken, so that the breasts are uniform in thickness and cook evenly on the griddle. Then, add the chicken breasts to the large bowl with the honey mustard sauce. Toss the breasts to coat them evenly with the sauce.
Heat griddle to about 350-375 degrees F.
Place chicken breasts on the hot griddle and allow to cook on the first side untouched for about 6-8 minutes, or until a nice golden brown color develops. Flip chicken to the second side and continue to cook an additional 5-6 minutes, or until the internal temp of each breast reaches about 160 degrees F.
While chicken is cooking, add about 1 tablespoon of cooking oil to a fresh area on the griddle. Saute the sliced mushrooms until tender and browned. Season with salt and pepper.
Divide the sautéed mushrooms between the four chicken breasts. Spoon on some of the reserved honey mustard sauce from step 1. Top each breast with an equal amount of shredded cheeses, chopped bacon, and sliced green onion. Spoon additional honey mustard sauce on top.
Continue to cook the loaded chicken breasts on the griddle until the cheeses are fully melted and the internal temp of each breast reaches 165 degrees F. *If needed you can use a melting dome to melt the cheese and/or elevate the chicken on a wire rack on the griddle surface.
As each individual piece of chicken reaches 165 degrees F, remove from the griddle. Serve warm with reserved sauce for dipping.