Preheat the oven to 400°F.
To prepare the marinade, combine mayonnaise, honey, Dijon mustard, and lemon juice in a bowl. Mix well until the marinade is smooth.
Place the chicken breasts in a resealable plastic bag or a shallow dish. Pour half of the marinade over the chicken, making sure each piece is well coated.
Allow the chicken to marinate in the refrigerator for at least 30 minutes. You can marinate it longer for more flavor if time allows. Reserve the remaining sauce for later.
In a large skillet over medium heat, cook the bacon until crispy. Remove the bacon from the skillet and set it aside.
Add sliced mushrooms and onions in the same skillet with the bacon grease, season with salt and pepper, and cook until the vegetables are tender and golden brown. Remove the mushrooms and onions from the skillet to the plate and set them aside.
In the same skillet, add butter and melt it over medium-high heat. Remove the chicken from the marinade and season the chicken breasts on both sides with salt and pepper.
Arrange the chicken breasts in the skillet in a single layer. Cook until they achieve a golden brown color on both sides, approximately 3 to 4 minutes per side.
Transfer the chicken to an oven-safe baking dish.
Place three bacon halves on each chicken breast.
Top each chicken breast with a portion of sautéed mushrooms and onions.
Sprinkle shredded cheddar and Monterey Jack cheese over the top.
Bake in the preheated oven for approximately 15 to 20 minutes or until the chicken is cooked through and the cheese is melted and bubbly.
Remove the dish from the oven and garnish with chopped fresh parsley.
Serve the Alice Springs Chicken hot with the reserved honey mustard sauce on the side.