Heat oven to 350°.
In a skillet, melt butter and oil and place chicken legs skin side down. Sear the chicken legs; flip once and sear the other side. Holding the legs in the pan with tongs, pour off excess fat into a dish before putting pan back over the flame. Pour bourbon over the chicken, then return pan to the flame; tilt the pan to ignite the whiskey.
Once flame subsides, add maple syrup and chicken stock to the pan, bring to a boil, and throw the whole pan into the preheated oven for 35 minutes. Remove pan from the oven, transfer the chicken to a heatproof platter and return to the oven to stay warm.
Place pan with cooking liquid on a high flame, bring to boil and reduce to a thick syrup. Take the syrup off the heat and swirl in a tablespoon of butter. Divide chicken among four plates and drizzle sauce on top. Garnish with chopped parsley and thyme.