Heat the beef drippings in a large skillet over medium heat until shimmering.

Whisk the all-purpose flour into the skillet to create a roux, cooking for 1 to 2 minutes until bubbly and lightly golden.

Gradually pour in the whole milk while whisking constantly to prevent lumps from forming.

Bring the mixture to a gentle simmer and cook until thickened, about 3 to 5 minutes.

Season generously with salt and coarse black pepper, adjust thickness with more milk if needed, and serve immediately.