With a small food processor or Ninja, grind the oats into finely chopped bits.
In a bowl, combine the ground oats, flour, corn starch, baking powder, salt, sugar and allspice. Use a pastry cutter to cut in the butter until crumbly.
Whisk together the milk and sour cream, then stir it into the dry ingredients to make a sticky, shaggy dough.
Scrape the dough out onto a well floured surface. Use floured hands to gently press the dough out to 1 inch thick, using a little more flour as needed to keep the dough from sticking.
Cut the dough into nine pieces with a bench scraper, stack the pieces, and press the dough out again to about 1 inch thick.
Cut into rounds with a 2 1/2 inch biscuit cutter, trying to cut as many bannocks as you can the first time. Do not twist the cutter, just cut straight down and lift it straight back up. Gather up the scraps, press them together and cut those as well. You should be able to cut around 12 bannocks.
Line a baking sheet with parchment paper, and place the bannocks close together, about 1/2-1 inch apart. Freeze the cut bannocks for 30 minutes.
While the bannocks are freezing, preheat the oven to 450 F and position a rack in the center of the oven.
Bake the bannocks until risen, fluffy and light golden brown on top, about 15 minutes.
Cool bannocks for 5 minutes, then serve hot with softened butter, jam or honey.