In a bowl, whisk together the honey, Dijon mustard, lemon juice, and paprika to make the honey mustard marinade. Reserve 1/4 cup of the marinade for serving.

Season the chicken breasts with salt and pepper. Place them in a large resealable plastic bag or shallow dish and pour the remaining honey mustard marinade over the chicken. Make sure the chicken is well-coated. Marinate in the refrigerator for at least 1 hour, or up to 4 hours for deeper flavor.

Preheat your oven to 375°F (190°C). Heat vegetable oil in a large oven-proof skillet over medium-high heat. Remove the chicken from the marinade (discard any leftover marinade) and sear the chicken breasts for 3-4 minutes on each side, or until golden brown.

Once the chicken is seared, top each breast evenly with the sliced mushrooms, then the cooked bacon slices (2 per breast). Sprinkle the Monterey Jack cheese and Cheddar cheese over the top of each chicken breast.

Transfer the skillet to the preheated oven and bake for 15-20 minutes, or until the chicken is cooked through (internal temperature of 165°F or 74°C) and the cheese is melted and bubbly.

Serve the Alice Springs Chicken hot, drizzled with the reserved honey mustard marinade. Garnish with chopped parsley or chives if desired.