Preheat the oven to 400 F.
In a small saucepan, mix the sour cherries with the red wine, sugar, pepper and thyme. Bring it to a boil.
While the cherries come to a boil, mix the corn starch with the cold water. once the cherry mixture starts to boil, pour in the corn starch slurry and stir constantly as the cherries come back to the boil and the mixture thickens. Remove it from the heat and set it aside while you prepare the rest.
Roll each sheet of puff pastry to approximately 12" by 10". It is important to roll the pastry a little bit even if the sheets you are using already fit this measurement. If you don't, the pastry will puff up quite a bit in the tins and your filling will go everywhere.
Using a cookie cutter, cut out twelve circles from each sheet of puff pastry. If you don't have a large enough cookie cutter, then simply cut each sheet of pastry into twelve squares. If you plan on cutting the pastry into squares then you should roll the pastry into a square as best you can.
Press the puff pastry into the wells of a mini tart pan or mini muffin tin.
Cut the goat cheese into 24 evenly sized pieces. Keeping it in the fridge until you need it will help you cut the goat cheese. Place the pieces of goat cheese into each tart.
Top the tarts with the cherry mixture. Each tart will get at least two cherries and some will get three. Spread the mixture out amongst the tarts as evenly as you can.
Bake at 400 F for 17-19 minutes or until the pastry is golden brown at the edges.
Let the tarts cool slightly in the pan and then remove them to a cooling rack. Serve warm or at room temperature.