Preheat oven to 400 degrees. Line a sheet pan with parchment paper and set aside.
Cut puff pastry into one-inch squares and place on a prepared baking sheet. Press the center of each square with your thumb or a teaspoon to make an indentation.
Divide goat cheese into the oven 40 pieces (about ½ teaspoon each). Place a piece of goat cheese into the indentation of each piece of puff pastry.
Transfer pan to oven and bake for about 15 minutes or until pastry is golden brown and puffed up.
While the pastry and goat cheese bake, add cherries, thyme, sugar, and sea salt to a small saucepan over medium heat. Cook until cherries begin to break down and release their juices (about 2 minutes).
Stir ingredients vigorously to dissolve sugar and sea salt in the liquid then cook until bubbling (about 3 minutes).
Reduce heat to medium low and let mixture simmer and thicken (about 10 minutes), stirring and pressing occasionally to break down cherries.
Spoon about ½ teaspoon of cherry mixture over each piece of baked puff pastry with goat cheese. Serve immediately while warm.
Can I make these goat cheese appetizers in advance? I recommend making this recipe shortly before serving as it is best enjoyed warm. You can, however make the cherry filling ahead of thyme and reheat it when needed.How to store extra? Place any leftovers in an airtight container and refrigerate. They will keep for up to five days this way.