For the goat cheese: Using a food processor, add the goat cheese, cream and thyme leaves and pulse until smooth. Season with salt and pepper. Refrigerate until ready to use.
For the tart tatin: Preheat the oven to 350 degrees F.
Give the cherry tomatoes a squeeze to remove the seeds. Divide the butter among each cup on a small muffin tray. Sprinkle them with sugar. Fill each cup with cherry tomatoes, adding a layer of sun-dried tomatoes in the middle. Cover loosely with foil and bake for 30 minutes.
Gently press down the tomatoes, molding them into the shape of the cups. Increase the temperature to 425 degrees F.
Roll the pastry out to 1/8-inch thick. Cut out circles to fit the muffin cups, and poke them all over with a fork. Top each cup with a pastry circle, pressing to seal. Bake until golden brown, 10 to 15 minutes.
Remove and let cool for 15 minutes. Run a small knife around the rims and invert the tarts onto a plate, topping with a small spoon of the thyme whipped goat cheese.