Whisk together the Dijon mustard, honey, mayonnaise, and lemon juice in a small bowl to prepare the marinade. Set aside ¼ cup of the mixture in a sealed container and refrigerate for serving. Place the chicken breasts into a large resealable plastic bag, pour in the remaining marinade, and ensure the chicken is fully coated. Refrigerate for at least 30 minutes or up to overnight.

Preheat the oven to 400°F. Melt the butter in a large, oven-safe skillet over medium-high heat. Add the sliced mushrooms and cook, stirring occasionally, until they have softened and browned, about 5 to 7 minutes. Remove the mushrooms to a bowl and wipe the skillet clean.

Add olive oil to the same skillet and heat until shimmering. Place the marinated chicken breasts in the skillet in a single layer, discarding excess marinade. Cook undisturbed until the underside develops a golden crust, approximately 5 minutes. Flip each piece and continue cooking for another 5 minutes, until evenly browned.

Evenly distribute the sautéed mushrooms atop the browned chicken. Sprinkle over the chopped bacon and top with the shredded cheese. Cover the skillet and transfer it to the oven. Bake for 10 to 15 minutes, or until the internal temperature of the chicken reaches 165°F at the thickest point.

Remove from the oven, garnish with chopped parsley if using, and season with salt and freshly ground pepper to taste. Serve with the reserved honey mustard sauce on the side for dipping.