In a large pot, heat oil over medium heat. Add onions, garlic and smoked drumstick. Saute until the onions become soft and the drumstick starts to brown, about 15 minutes.
Turn off heat. Add bourbon, thyme and sage. Turn heat back on to medium-high. Let simmer for a couple minutes to burn off some of the alcohol.
Add 4 cups of stock and bring to a boil. Let simmer for about 20 minutes.
Remove drumstick and strain gravy through a fine mesh sieve.
In pot, melt butter. Add flour and whisk until smooth. Allow to cook until light brown. It will be a paste.
Slowly pour strained gravy back to the pot and turn on heat to medium. Whisking constantly until the flour is incorporated into the liquid.
Simmer over medium heat for about 20 more minutes or until the gravy begins to thicken.
Season with salt and pepper if needed. If you are not tasting the Bourbon then add 1 Tablespoon at the end and let simmer for about 10 minutes to let the alcohol burn off.