Prepare the puff pastry: Lay it out on a cookie sheet lined with parchment paper. Trim approximately 1/2 inch around the edge of the puff pastry sheet. Use those trimmings to create a "frame" around the edge of the puff pastry sheet.

Mix the egg yolk with a few drops of water, and then brush the egg yolk lightly around the edge pieces. Use a fork to prick a few holes in the puff pastry. Bake at 400 degrees for 20 minutes, or until puffed up and lightly browned.

Meanwhile, mix together the goat cheese and milk and add salt and pepper to taste. When the puff pastry comes out of the oven, spread the goat cheese mixture thinly and evenly over the center of the pastry. Top with tamarillo slices.

Bake for another 5 minutes. Remove from oven and top with basil pieces. Serve warm or at room temperature.