Combine 1 cup flour, yeast, sugar and salt in a large bowl. Add water and 3 tablespoons oil and stir for about 1 minute or until well blended. Gradually add enough remaining flour to make a soft dough. Dough should form a ball and will be slightly sticky.
Knead by hand on a floured surface, adding additional flour as necessary, until smooth and elastic, about 4 minutes. Let dough rest at this point for 10 minutes.
Roll dough out to about 1/8 inch thickness. Pierce all over with a fork 10-12 times, then bake in preheated oven for 5 minutes. Meanwhile make the cheesecake layer.
Cream together cream cheese, sugar, and eggs. Spread all over crust, then return to oven for another 10 minutes or until cheesecake layer is set.
Top with berries. Whisk together powered sugar, milk, and vanilla, adding more milk as needed to thin to desired consistency. Drizzle over berries. Sprinkle with cinnamon sugar, cut, and serve.