Melt the unsalted butter in a medium saucepan over medium heat until it’s completely melted and bubbly.
Sprinkle in the all-purpose flour, then whisk constantly for 1–2 minutes until the roux turns light golden brown and smells nutty.
Slowly pour in the beef broth a little at a time, whisking vigorously as you go to prevent lumps.
Bring the gravy to a gentle simmer over medium heat, whisking occasionally, and let it simmer for 3–5 minutes until it reaches your desired thickness.
Remove the saucepan from the heat, stir in the salt and black pepper, taste and adjust seasoning if needed, then serve the gravy hot.