Heat bacon drippings in a skillet over medium heat; whisk flour into drippings until smooth. Reduce the heat to low and cook, stirring constantly so it doesn't burn, until roux is caramel brown in color, about 15 minutes. Stir in salt and black pepper.

Add milk, 1/2 cup at a time, whisking until thoroughly blended after each addition. Bring gravy to a simmer, then whisk constantly until thick, smooth, and bubbling.