Thaw the puffed pastry on the counter for 45 minutes or in the fridge for several hours.When thawed, carefully open the sheet, then slice it in half down the middle. Place both halves on a baking sheet lined with parchment or a baking mat. Preheat oven to 415 degrees, then start on the pizza toppings.In a large skillet over medium-high heat, saute mushrooms and garlic in the butter for 2 minutes, then pour in the wine and season with salt and pepper. Allow to continue cooking for 5-7 minutes, until mushrooms are cooked down and liquid is mostly gone. Remove from heat and set aside.To build the pizzas: Brush a thin layer of olive oil in the center part of each half of puffed pastry.On each half, sprinkle on half the cheese so that it covers all but a 1/2 inch border all around the pastry.On one half, sprinkle on the cooked mushrooms. On the other half, sprinkle on the halved tomatoes. Press both mushrooms and tomatoes lightly into the cheese.Place the pan in the oven and bake for 15 minutes pastry could go crazy and puff up in areas here and there, but don't worry! It'll be fine. Remove from the oven and sprinkle the goat cheese crumbles on both halves. Allow the pizzas to sit for 10 minutes. If there are any big air bubbles/puffs, just give them a little smush or wait and they'll calm down.Sprinkle on basil, slice into pieces, and serve!