In a pot over medium high heat, add the water and the salt. Stir until salt has dissolved, remove from heat, add the beer and ice. Stir until ice has dissolved and brine is at room temperature or below.

Add the chicken quarters to a large bowl. Pour the brine over the chicken, cover loosely with plastic wrap, refrigerate for 3 hours and up to 24 hours.

Preheat oven to 425F.

Add the stout, mirin, soy, chili powder, cornstarch and honey, whisk to combine. Add sauce pan to high heat, allow to boil until slightly reduced and thickened, about 5 minutes.

Cover a baking sheet with aluminum foil, place a wire rack over the foil lined baking sheet.

Remove chicken from brine, discard the brine. Rinse the chicken well and pat dry. Place chicken on the wire rack.

Brush liberally with the glaze.

Roast at 425F for 45 to 55 minutes, brush with glaze every 10-15 minutes. Remove from oven when the internal temperature reaches 175F.

While the chicken is cooking make the sweet potatoes. In a saucepan, melt the butter with the oil over medium heat. Add the shallots and cook over medium-low heat until caramelized, about 20 minutes.

Boil the potatoes in a pot of lightly salted water until fork tender, about 12-15 minutes. Drain, return sweet potatoes to the dry pot. Add 4 tbs butter, cream, maple syrup, salt, and nutmeg, mash with a potato masher until well combined and potatoes are well mashed, transfer to a serving dish. Top with caramelized shallots, chopped pecans and drizzle with balsamic glaze.