Preheat oven to 425 F and grease 9 inch pan with butter or butter spray.
In a medium bowl combine ingredients for filling: brown sugar, white sugar and cinnamon. Mix together. Add vanilla extract and butter. Mix until all ingredients are well combined.
In a large bowl mix ingredients for the dough: flour, sugar, baking powder, baking soda and pinch of salt. Add buttermilk, milk and melted butter. Knead the dough by hand for a minute. If the dough will become sticky, dust with flour your surface or hands.
Lightly flour the work surface. Using your hands make a rectangular from the dough (about 0,5 inch thick).
Spread 2 Tbsp. softened butter on the rectangular. Spread the filling evenly on the rectangular. Roll it to shape a log and cut about 8 sections.
Lay nicely on the baking pan. Brush rolls with remaining 2 Tbsp. melted butter.
Bake in temperature 425 F for 15 minutes, then reduce temperature to 350 F and bake for another 10 minutes.