For the chicken brine: Combine 1 cup water, the honey, salt, bay leaves, garlic and thyme in a large saucepot. Bring to a boil over medium-high heat. Once at a boil, turn off the heat and add the ice cubes. Place the chicken and brine into a large resealable gallon plastic bag. Refrigerate, brining the chicken, for 1 hour.
For the honey glaze: In a small saucepot over medium-low heat, whisk the honey, vinegar and orange juice until just simmering. Remove from the heat and set aside at room temperature until ready to use.
For the chicken: Once brined, remove the chicken quarters from the bag and pat dry. Sprinkle the chicken with the salt and pepper and place skin-side down into a cast-iron pan. Place into the oven. Roast until the internal temperature reads 155 degrees F, about 50 minutes, flipping halfway through the baking time. Remove from the oven, brush the chicken with the honey glaze, and then return to the oven. Finish roasting the chicken until the skin is crispy and the internal temperature reads 165 degrees F, about 15 minutes. Remove the chicken and allow to rest about 10 minutes. Reserve the pan drippings.
For the gravy: To the same cast-iron pan, over medium-high heat, add the olive oil. Add the mushrooms, garlic and shallots, and toss to combine. Allow to soften, being careful not to burn. Season with salt and pepper. Add the flour and whisk to incorporate with the fat. Continue cooking out the starch for about 2 minutes. Add the white wine and scrape up any browned bits on the bottom of the pan. Reduce for about 1 minute. Add the chicken stock and reduce by half, 2 to 3 minutes. Remove from the heat and drizzle in some truffle oil. Swirl in the butter. Season with salt and pepper. Arrange the chicken pieces on a serving dish, finishing with the truffle gravy.