Remove the sheet of puff pastry from the freezer and set out until it comes to about room temperature - 20 to 40 minutes depending on how warm your kitchen is. Preheat oven to 400F and line a baking sheet with parchment paper.
Mix goat cheese, heavy cream and grated garlic together until a smooth mixture remains. Cut tomatoes into thin slices - about ⅛” thick.
Roll puff pastry sheet into a 12”x14” rectangle and place on the lined baking sheet. Puncture sheet of puff pastry all over with a fork.
Spread goat cheese mixture over the puff pastry and layer on the sliced tomatoes in an even layer. Season the tomatoes with salt and pepper.
Place in the oven and bake at 400F for 18-20 minutes.
Grate fresh parmesan cheese over top and garnish with fresh basil. Allow to cool slightly before cutting into 9 slices and serving.