Season chicken breasts with salt and pepper and place in resealable bag. Pour buttermilk into bag and refrigerate at least 1 hour or overnight.
Place flour on plate and season with salt and pepper. Pour wing sauce into bowl. Heat large sauté pan over medium-high heat. Add vegetable oil to about 1-inch depth and heat to 350°F. Remove chicken breasts from bag and roll in flour to coat. Fry in hot oil, 4-5 minutes per side, until golden and cooked through.
Remove chicken breasts from skillet with tongs and turn them in the bowl of wing sauce to coat evenly. Reserve on plate.
Heat large skillet over medium heat. Butter one side of each bread slice. Place 4 slices, butter-side down, in skillet and top each with 1 slice Monterey Jack, 1 chicken breast, 1 ounce Blue cheese crumbles, and 1/2 cup of shredded lettuce. Top each sandwich with another piece of the bread, butter-side up, and grill, turning once, until bread is golden and cheese melts.