In a small sauce pan over medium heat, add olive oil and shallot. Stir often so as to not burn the shallots. This should take about 4 minutes. Add garlic and sauté an additional 1 minute.
Add remaining glaze ingredients in the pan and stir to incorporate. Bring heat up to medium high and a simmer. Continue to simmer the glaze for an additional 20 minutes or until the glaze has reduced in half.
Remove the glaze from the heat and allow to cool. As the glaze cools, it will thicken up with the flavors getting more intense. You can place in the refrigerator until ready to use. We recommend doing this prior to starting the grill so it has enough time to cool and thicken.
For the Grilled and Glazed Chicken
Remove any excess fat from the chicken. Coat chicken in olive oil and liberally apply the poultry seasoning. Can be done up to 24 hours prior to cooking.
Prepare the grill for two-zone cooking method targeting 450 - 500 degrees ambient cooking temperature in the grill.
Place the chicken over direct heat on the grill and cook until it gets a nice sear (about 4 minutes with the lid closed). Flip the chicken and grill the other side over direct heat for an additional 4 minutes with the lid closed to get a nice sear on that side. Then move to indirect heat.
Continue to grill over indirect heat with the lid closed. When the chicken reaches an internal temperature of 150 degrees Fahrenheit (about 8 minutes), glaze the chicken once. Continue to grill over indirect heat and remove from grill when the internal temperature of each piece is at least 165 degrees Fahrenheit.
Immediately glaze the chicken one last time and let rest 10 minutes loosely tented with foil. Serve with your favorite side.
A note about grilling chicken: Every piece will cook at different times. They key is watching each piece to be sure it doesn't burn and is removed when the internal temperature is to your desired minimum temperature.