Heat oven to 375°. Working with one sheet at a time, cut circles from the pastry using a 2½-inch round cutter. Gently fit the rounds into the cups of 1½ mini-muffin pans (about 36 cavities, total) so that the dough is flush with the edge of each cup. Prick all over with a fork and refrigerate until cold, about 15 minutes.
Meanwhile, combine the goat cheese and sour cream in a medium bowl. Slowly stir in the heavy cream until the mixture is completely smooth. Season with salt and pepper.
Heat the olive oil in a small skillet over medium heat. Add the shallot and cook, stirring occasionally, until translucent, about 4 minutes. Add the vinegar and thyme leaves and cook until the vinegar is mostly absorbed. Let cool slightly, then season with salt and pepper. Transfer to a small bowl and fold in fig jam.
Remove the muffin pans from the refrigerator. Fill each cup with one heaping tablespoon of the goat cheese mixture. Bake until the pastry is slightly puffed and golden brown, 15-20 minutes, rotating the pan once halfway through. Let the tartlets cool in the pan for 5 minutes, then transfer to a platter.
Top each tartlet with 1 walnut piece, 1 teaspoon fig compote, and a small pinch of micro greens. Serve at room temperature.
These look like tasty little morsels. Wondering if I could just use mini premade phyllo cups and fill with goat cheese mixture.
35 ounces of puff pastry sounds like a lot. Could it be 3.5 ounces instead?