Combine the water, red pepper flakes, ground mustard, kosher salt and bay leaves. Warm over medium heat until the salt and mustard have dissolved. Remove from the heat and add the thyme, sage and Worcestershire. Stir to combine and let cool for 15 minutes.
Meanwhile, place the olive oil, tarragon, basil and garlic into a food processor. Blitz until a loose paste is formed. Add the olive-oil herb mixture into the brine (the water-salt mixture). Stir to combine the newly formed marinade.
Once the marinade is at room temperature (to speed up the cooling process, I add a few pieces of ice), place the chicken into a large sealable plastic bag. Pour the marinade over the chicken. Place the chicken into the fridge and marinate for at least 8 hours or up to 24 hours. Be sure to flip the plastic bag every 2 to 3 hours to ensure even marination.
When ready to cook, heat the grill to 400 degrees. To achieve this, set up your grill for indirect cooking at 350-400°F. This can be done in several ways depending on your grill setup. The simplest method for a charcoal grill is to push your charcoal pile to one side of the coal area and place the chicken on the other side atop the cooking grate. This will require you to turn the chicken during the cooking process to cook the exterior evenly. For a gas grill, use the same approach, only using a portion of the burners for heating and keeping the chicken on the other side, also rotating as necessary. Keep in mind that in order to grill chicken vertically, the lid of the grill will have to be able to close over the height of the chicken.
Remove the chicken from the marinade and place onto a vertical chicken roaster. Set the marinade aside.
Place the chicken onto the heated grill. Close the grill lid and roast for 45 minutes to 1 hour, or until the chicken has reached an internal temperature of 165 degrees. Turn the chicken about halfway through. Remove the chickens from the grill and let rest for 10 minutes.
Meanwhile pour the marinade into a small saucepan and bring to a boil over medium heat and then reduce to a simmer. Once simmering, remove 1/2 cup of liquid and place into a small bowl. Add the corn starch and whisk until it has dissolved. Pour the slurry back into the simmering marinade, whisking to combine. Continue to let simmer until thickened. Keep warm.
Cut the chicken into serving portions and serve with a small side of thickened pan sauce.