Preheat the oven to 350 degrees F. Line a baking sheet with parchment paper.
Using a rolling pin, roll out the pizza dough to a thickness of about 1/4 inch. Transfer the pizza dough to the lined baking sheet and brush the dough with the melted butter. Sprinkle with 2 tablespoons Cinnamon-Sugar and bake until golden brown, about 10 to 15 minutes. Cool the pizza crust on a wire rack.
Meanwhile, in a medium bowl, mix together the cheese, cream, lemon juice, and zest.
Spread the cheese mixture over the cooled crust. Top with mixed berries and sprinkle with the remaining Cinnamon-Sugar. Slice like a pizza and serve.
Cut the vanilla bean in half, lengthwise. Using the back of a knife, scrape along the inside of the vanilla bean to collect the seeds. Scrape vanilla bean seeds into a small bowl. Add sugar and cinnamon and stir to combine. Set aside in a small serving bowl.