Combine the chicken broth, Greek yogurt, heavy cream, and Dijon mustard in a medium bowl. Stir to combine and set aside.

Add the butter to a small skillet set over medium heat. Stir occasionally until melted. Slowly whisk the flour in a little at a time until completely blended into the butter without any lumps remaining.

Stir in the yogurt mixture and season with salt and black pepper, to taste. Cook for several minutes, whisking continually, until the sauce thickens and is heated through. Remove from heat and keep warm.