Blitz the coarse cornmeal to a fine consistency in a food processor or blender. Sift to obtain soft, superfine cornmeal flour.
Mix with the all-purpose flour and salt in a large bowl. Add butter, sugar, & bergamot flavour drops to a blender and blend to a smooth, buttery paste.
Add butter mixture to flour mixture and knead the dough by hand until it comes together as one blob. Cover with plastic wrap and chill in the fridge for 30 minutes.
Take out after chilling and knead by hand again until it forms a soft, malleable dough at room temperature. Roll as much dough as you plan to use into a ¼” thick sheet and cut out small 1” circles with a cookie cutter. If you don’t want to use all the dough at the same time, tightly cover the unused portion in plastic wrap and freeze for up to 3 months for future use.
Lay the cookie cutouts on a baking sheet lined with parchment paper and freeze for 45 minutes. Meanwhile, preheat the oven to 350° F. Once freezing time is up, bake the shortbread for 8-10 minutes until the edges turn golden-brown (this is a good time range to bake 8-12 shortbread cookies).
The centers might still be soft, but don’t worry – they will harden as they start to cool at room temperature on a wire rack.