1Preheat oven to warm, 170 degrees F.
Place butter, buttermilk, oil and water into a small pan. Heat until butter is melted and temperature in 115-120 degrees F.
2In a large bowl mix flour, sugar, yeast and salt together. Add warm milk mixture and eggs. Mix to form slightly sticky dough. Transfer dough to a lightly floured countertop. Lightly flour and roll out to large rectangle about 1/4 inch thick.
3On surface of dough spread butter. Mix together brown and granulated sugar with cinnamon and sprinkle over surface. Tightly roll flat sheet. Cut into 8 pieces. Flatten each piece and place on oiled baking sheet. Cover with plastic and let rise 30-45 minutes.
4Remove plastic and bake at 350 degrees 25-30 minutes until browned. Remove from oven and let cool 10 minutes.
5Mix together powdered sugar, butter and vanilla. Mix milk in a few drops at a time to form a thick icing. Spread over cooled rolls.