Preheat oven to 400°F. Line a large rimmed baking sheet with parchment paper.
Roll out puff pastry dough. Cut each section into four even rectangles. Set rectangles approximately ¼ inch apart on baking sheet. Bake for 15 to 25 minutes, or until golden. Place on cookie rack to cool. Pastries will deflate slightly.
In a bowl, combine goat cheese, cream cheese, honey, and pepper. Using a mixer on medium speed, blend until ingredients are well combined. Fold in chopped strawberries and basil.
When pastries are cool enough to handle, cut in half horizontally. Spread strawberry mixture evenly onto each pastry. Top with sliced strawberries and sprinkle with basil.