Preheat oven to 425° F. Line a baking sheet with parchment paper.
In a large bowl, whisk together the flour, sugar, baking powder and salt.
Use a box grater to grate the cold butter after it has been in the freezer for 30 minutes. Add the grated butter to the bowl with the flour mixture and mix in gently with a fork.
Combine the 3/4 cup heavy cream, 3/4 cup whole milk, and vanilla in a liquid measuring cup. Pour into the dry ingredients and use a fork to mix gently until the dough starts to come together. Try not to over-work the dough. It may be sticky.
Transfer the dough to a floured work surface. Press the dough into a rectangle that is about 3/4-inch thick, adding a little flour on top of the dough if it's too sticky. Fold the dough in half and then press it into a 3/4-inch thick rectangle again. Repeat this 2-3 more times.
When you have pressed the dough into a 3/4-inch thick rectangle for the last time, you are ready to cut out your biscuits. Press a 3-inch biscuit cutter (or upside down glass) straight down into the dough without twisting. Cut out as many biscuits as you can and place them on the parchment-lined baking sheet. It is ok if the biscuits are close together.
Reshape the dough scraps to cut out more biscuits.
Brush the tops of the biscuits with a little bit of heavy cream. Sprinkle with turbinado sugar, if desired.
Bake for 13-15 minutes, or until biscuits are golden on top.