Preheat the oven to 425°F. Pluck the grapes from their stems and wash. Dry the grapes as well as you can and transfer to a small baking sheet. Drizzle with the olive oil, balsamic vinegar, and honey. Roll the grapes around to coat them evenly.
Season with kosher salt and pepper. Roast for 30 to 35 minutes until the grapes begin to burst and release their juices. Remove and let cool slightly before using. The grapes can be made ahead of time and rewarmed before serving.
Line a baking sheet with parchment paper and set aside. Unroll the puff pastry sheets and cut out 8 large circles, 4 circles per sheet. Transfer the pastry circles to the baking sheet.
Run a sharp paring knife around each circle, creating a ¼-inch border, being careful not to cut completely through. Use a fork to dock the pastry several times inside the border.
Crumble the goat choose onto each tart, covering the base as evenly as possible while leaving the border clear. Sprinkle the goat cheese with the fresh thyme, kosher salt, and pepper. Drizzle very lightly with a little olive oil.
Make an egg wash by whisking together the egg and water. Brush the borders of each tart with the egg wash.
Bake the goat cheese tarts at 425°F for 20 to 25 minutes until the pastry is golden brown and cooked through. Check the tarts after 10 minutes and if they are puffing too much, poke them with a paring knife so they deflate.
To serve, transfer the warm tarts to a serving platter. Top with a spoonful of roasted grapes and drizzle with some of the roasting juices from the grapes. Garnish with fresh thyme leaves and enjoy!