Strain the pan drippings into a large measuring cup and let stand 5 to 10 minutes so the fat rises.
Pour 1 cup broth into the hot roasting pan and scrape up the browned bits for 1 to 2 minutes. Add this to the drippings.
Spoon 6 tablespoons of fat into a medium saucepan, adding butter if there is not enough.
Add broth to the drippings to make 4 cups of liquid in total, and warm it.
Heat the fat over medium heat, whisk in the flour and cook, whisking, for 2 to 3 minutes until light golden.
Whisk in the warm liquid about 1 cup at a time until smooth.
Bring to a gentle boil and simmer 5 to 8 minutes, stirring often, until it coats a spoon. Stir in the herbs, taste, then season with salt and pepper. Strain if you like.