Make the roux. Melt the butter in a large skillet over medium heat. Add the rice flour and whisk until combined and clumpy. Cook, stirring frequently, until the mixture turns golden brown and nutty-smelling, about 2-3 minutes.
Add the meat drippings and fresh herbs, if using. Stir to combine, breaking up any drippings that have solidified.
Combine and simmer. Pour in 2 ½ cups of the chicken broth and bring to a simmer. Cook for 2-3 minutes, stirring constantly with a whisk, until thickened.
Strain the gravy through a sieve into a measuring cup to remove any solids like the herbs. Season with salt and pepper to taste.
Serve. For serving, thin the gravy with more broth until the desired consistency is reached. For storage, refrigerate strained gravy for up to 4 days before reheating with remaining broth.
When reheating, avoid the microwave to prevent overcooking or curdling. Opt for the stove on low heat, stirring frequently, and remove it once it simmers.
