Tarragon and Thyme White Wine Bechamel Sauce

Tarragon and Thyme White Wine Bechamel Sauce
1 pound unsalted butter
3 cups all-purpose (plain) flour
2 cups white wine
4+ cups of milk (I used 2%)
2 Tablespoons unsalted butter
2 large onions, finely diced
2 stalks of celery, finely diced
1 cup chopped fresh tarragon
1/2 cup chopped fresh thyme
salt and pepper, to taste

In a large saucepan over medium heat, melt the butter. Add the flour all at once and whisk vigorously until smooth. Gradually pour in the wine, whisking constantly until liquid is absorbed by the flour. Add in the milk. Cook over medium heat, whisking ocasionally until thickened and the taste of flour is cooked out. 
Meanwhile, in a large frying pan over medium heat, melt the remaining two tablespoons of butter. Add the onions and celery, cover, and turn to low heat. Allow the vegetables to sweat, without coloring, until softened. 
Stir the vegetables unto the sauce along with the herbs, then season to taste. 

The bechamel sauce is now ready. It can be used as a base for any kind of gratin, or it can be thinned out with some more milk or enriched with cream and/or butter to be used as a sauce.