In a mixing bowl, combine whole wheat flour, protein powder, baking powder, and salt. Mix well.
Add melted coconut oil, honey, egg, and vanilla extract to the dry ingredients. Mix until a dough forms.
Wrap the dough in plastic wrap and refrigerate for 15 minutes.
Meanwhile, prepare the filling by combining mixed berries, Greek yogurt, cornstarch, and water in a small saucepan. Cook over medium heat until thickened, then let cool.
Preheat the oven to 350°F (175°C). Roll out the chilled dough on a floured surface to about ¼ inch thick. Cut into rectangles.
Place a tablespoon of the berry filling in the center of half the rectangles. Top with another rectangle and seal the edges with a fork.
Transfer the tarts to a baking sheet lined with parchment paper and bake for 20 minutes or until golden brown.
Allow to cool slightly, dust with powdered sugar, and serve warm.