In a saucepan, bring the wine, port, black peppercorns, shallot, thyme, and sugar to a boil, stirring until the sugar dissolves. Add the citric acid.
Cook over moderate heat, without stirring, until syrupy and reduce to 1 cup, about 35 minutes.
Strain and discard the solids. Let the caramel cool slightly.
Whip 3/4 c. of cream on medium speed in a standing mixer until it reaches stiff peaks. Move to another bowl and chill.
Add goat cheese and remaining 1/4 c. cream to standing mixer and switch to paddle attachment. Beat on medium high speed until the goat cheese softens, about 5 minutes, scraping down the sides of the bowl.
Increase speed to high and mix for 4-5 minutes scraping down sides once during the process. Fold in the whipped cream in four increments and season to taste.
Adapted from The Kitchen at Middleground Farms