Make the gravy base: Melt the butter in a large saucepan over medium-high heat. Add the flour and cook, whisking, until smooth and golden brown, 4 to 5 minutes. Whisk in 3 cups of the broth, 1 teaspoon salt, and ¼ teaspoon pepper and bring to a boil. Reduce heat and simmer until thickened, 1 to 2 minutes.
Discard the vegetables from the reserved roasting pan and strain the pan drippings into a large measuring cup or bowl. You should have about 1½ cups of liquid. Let stand for 5 minutes, then skim off and discard the fat. (Alternatively, use a fat separator.)
Place the empty roasting pan across 2 burners. Add the bourbon and cook over medium-high heat, scraping up the bits stuck to the pan, for 1 minute. Add to the gravy base in the saucepan, along with the strained drippings, and cook until warmed through, 2 to 3 minutes.
Strain, if desired, and adjust the consistency with additional broth if necessary before serving.