In the same skillet, melt 2 more tablespoons butter. Whisk in 2 tablespoons flour. Stirring constantly, cook over medium heat until the flour smells like baked pie crust, about 3 minutes. Slowly whisk in milk, about 1/2 cup at a time, then whisk in nutmeg, cayenne pepper, and thyme. Bring to simmer, and cook until thickened, whisking constantly, 3 more minutes. Transfer to a bowl and reserve.