Melt the butter in a saucepan over medium heat.

Add the flour and whisk until smooth. Cook for 1-2 minutes, stirring constantly, until the mixture turns light brown.

Slowly add the broth to the pan, whisking constantly to prevent lumps from forming.

Add the heavy cream, tarragon, salt, and pepper to the pan and stir to combine.

Bring the sauce to a simmer and cook for 5-7 minutes, stirring occasionally, until it thickens and coats the back of a spoon.

Remove the pan from the heat and let the sauce cool for a minute or two.

Serve the sauce over chicken or fish.