First, make the reduction. Melt 1 tablespoon of the butter in a large saucepan over medium-low heat. Add the diced shallot and cook until softened, about five minutes. Then, add all of the port and the thyme sprigs, and bring to a boil over high heat. Watch for the boil, then reduce the heat to maintain a brisk simmer. Cook until the port has reduced to the consistency of corn syrup, about 30 minutes.
At the same time, bring the chicken broth to a simmer in a small saucepan. Once it's brought to a simmer, turn off the heat, and add the redcurrant jelly.
Add the enriched chicken stock to the port reduction. Bring the sauce to a boil over high heat, then reduce to maintain a brisk simmer. Cook until it's reduced to about ⅓ its original volume, which is about 15 minutes. Strain again through a fine strainer, pressing on the solid shallots. Add salt and pepper to taste.
Bring the sauce to a low simmer, stir. In a separate bowl, mix the flour and butter into a paste, then whisk rapidly into the simmering sauce to thicken it. Whisk for 2 minutes to give the sauce a single consistency. Raise the temperature to a simmer, and maintain that while whisking for 2-3 minutes to remove any flour flavour. Add a teaspoon or so of fine balsamic vinegar, and taste a few times.
