Preheat the Oven: Set your oven to 350°F (175°C).

Prepare the Filling: In a large bowl, mix the sugar and cornstarch. Add the blueberries, lemon juice, and vanilla extract. Stir until well combined, then transfer the mixture to a lightly greased 9 x 13-inch baking dish.

Make the Biscuit Topping: In a separate large bowl, whisk together the flour, sugar, baking powder, baking soda, and salt. Add the cold, shredded butter and mix until the mixture resembles coarse crumbs. In a small bowl, combine the sour cream, milk, and honey. Add this mixture to the dry ingredients and stir until just combined; the dough will be slightly crumbly.

Assemble the Cobbler: Spoon the biscuit dough over the blueberry filling, covering most of the surface.

Prepare the Biscuit Finish: In a small bowl, whisk together the egg and milk. Brush this egg wash over the biscuit topping, then sprinkle with coarse sugar.

Bake: Place the baking dish in the preheated oven and bake for 45–55 minutes, or until the biscuit topping is golden brown and the filling is bubbling.

Cool and Serve: Allow the cobbler to sit for about 5 minutes before serving. Serve warm, ideally with a scoop of vanilla ice cream.