Preheat the oven to 350F.
Heat the olive oil in a skillet over medium high heat. Add the onions, cooking until starting to brown. Stir in the garlic, mushrooms, salt and pepper.
Cook, stirring occasionally, until the mushrooms are dark and softened, about 10 minutes. Sprinkle with flour, stirring for about 30 seconds.
Add ½ cup beer, cooking until the beer is gone, about 15 minutes.
Lay the chicken thighs on a flat surface. Trim away any excess fat. Cover with plastic wrap, pound to an even thickness with a meat mallet, rolling pin or heavy skillet.
Add one to two tablespoons of filling to the center of the chicken thighs, roll into a log.
Gently transfer chicken to a baking dish, seam side down.
In a small bowl stir together the hoisin sauce and remaining tablespoon beer.
Brush the chicken with sauce, bake for 15 minutes, re-brush with sauce and continue to bake until chicken is cooked through, about 10 additional minutes.