Place chicken on a large cutting board, breast-side down. Using kitchen shears, cut along each side of the backbone and remove (save this to make bone broth).
Flip over; press firmly with your palm in center of breasts to flatten.
Whisk together mustard, mayonnaise, rosemary, and lemon juice.
Season chicken generously with salt and pepper, then slather both sides with mustard mixture.
Cover loosely and let stand while you prepare the grill (or refrigerate in a resealable bag up to 24 hours. Return to room temp 1 hour before grilling).
Heat grill to 350 degrees. for direct and indirect cooking. Oil grates over indirect grilling zone, then place chicken, skin-side up, on grill with legs facing direct zone (this prevents the breasts from overcooking before the legs are done).
Cover and cook, maintaining a temperature of about 350 degrees, until skin begins to brown and a thermometer inserted into the thickest part of the breast reads 150 degrees.; about 45-50 minutes.
Oil grates over direct-heat zone. Using tongs, flip chicken skin-side down over direct heat. Cook, moving occasionally to avoid flare-ups, until skin is charred in places and chicken is cooked through (thermometer should read 160 degrees); 5-10 minutes more.
Transfer to a tray. and cover with foil. Let stand at least 15 minutes before serving.