To make the marinade, in a small bowl, whisk together mustard, honey, and salt and pepper to taste (I like 1 teaspoon salt and 1/2 teaspoon pepper). Reserve 1/4 cup mustard mixture for basting the chicken. Transfer the remaining mixture to a 1-gallon zipper-lock bag.
To butterfly the chicken breasts, cover a cutting board with a piece of plastic wrap. Add chicken breasts. Working with one breast at a time, place your palm on top of the breast and slice in half horizontally, stopping 1/2-inch from the edge so the pieces are attached.
Transfer chicken to the bag with the mustard mixture. Repeat with remaining pieces of chicken and mash to coat. Refrigerate for at least 30 minutes or up to 1 hour.
Preheat grill over high heat until hot; reduce heat to medium-high. Clean and oil cooking grate. Place chicken over direct heat and onions over indirect heat. Cover and cook until the chicken is lightly charred, about 5 minutes. Flip onion slices and chicken.
Brush chicken with reserved mustard mixture, cover, and cook until lightly charred on the second side, about 5 minutes. The chicken must register degrees on a thermometer. Move chicken to indirect heat side. Divide onion rings evenly among chicken breasts, then top with bacon and cheese.
Cover and cook until pepper Jack is melted and chicken registers 165 degrees, about 2 minutes longer. Transfer chicken to a platter, tent loosely with aluminum foil, and let rest for 5 minutes. Serve with lime wedges and Pico de gallo.