Cook and drain the egg noodles according to package directions and set aside.
Place the butter in a small saucepan and heat over medium heat until it begins to foam. Whisk in the flour and cook until the mixture develops a pale golden color, about 3 minutes.
Slowly add the milk, then the chicken broth, whisking continually until the sauce is smooth and thickened, 2 to 3 minutes longer.
Whisk in the vinegar, a pinch of sugar and the sour cream until smooth, then stir in the dill, reserving a little for garnish.
Cook the sauce for another 2 minutes, stirring continually, and season to taste with salt and pepper.
Combine with the noodles and transfer to a serving dish. Garnish with the reserved dill.
Tips for Making This Recipe
Dried dill can be substituted - just reduce the quantity to 1 to 2 teaspoons.