In a large pot pan set to medium-high heat add olive oil and your smoked turkey drum and shallots. Season with salt and pepper. Continue to stir and rotate the drum until it’s browned on all sides and you start to see some drippings in the pan, and your shallots have softened (about 10 minutes).
Add garlic and cook for 1 minute and then reduce heat.
Add bourbon and let simmer for two minutes (if the pan is still really hot it’ll boil, so be sure to avoid too much heat causing it to nearly evaporate).
Add the thyme and 4 cups of stock and bring back to a boil (reserving the 5th cup for later). Cover and let simmer for 25-30 minutes.
Meanwhile make your slurry: take the remaining 1 cup of stock and place it in a sealed jar with the flour. Shake vigorously until all of the flour has been fully absorbed.
After 25 – 30 minutes remove the smoked turkey drum from the pan and set aside. The stock will have reduced and absorbed a smoky flavor.
Add the slurry to the pan, and begin whisking. Continue whisking while the gravy begins to thicken (about 10 minutes). If it gets too thick add more stock. If it’s too thin, let it simmer a few more minutes. It will thicken up after you remove it from the heat. Salt and pepper to taste again.
Strain before serving.