Using a narrow boning knife, make a slit along the side of one of the chicken breasts, almost cutting through all the way through the side. Repeat with remaining chicken.
Place stuffing inside a gallon size zip-top bag. Snip a small hole in one of the corners. Squeeze to dispense. Stuff each chicken breast until slit fills up halfway. Brush opening edge with Dijon mustard and press down lightly.
Coat chicken with mustard and season liberally with Grill Seasoning. Massage seasoning in.
Quickly swab grill with oil soaked towel. Grill chicken over a preheated charcoal grill, turning often, until area under stuffing reaches 165°F (75°C) and stuffing reaches 165°F (75°C).