Preheat the oven to 375.
In a large baking dish, toss the blueberries, 1/2 cup sugar and tapioca together.
Stir the lemon juice and milk together and allow to sit for 5 minutes.
In the bowl of a food processor, pulse together the flour, sugar, baking powder, baking soda, and salt. Pulse the butter into the dry ingredients until course crumbs form. Stir in the milk mixture gently until a soft dough forms.
Use an ice cream scoop to drop the dough evenly over the berries.
Bake in the preheated oven for 35 minutes, or until the top is golden brown. Place a baking sheet on a rack underneath to catch any overflow.
To make the creme anglaise: In a large bowl, vigorously whisk the egg yolks and sugar together until pale yellow. Warm the milk and cream in a saucepan on the stove, then slowly pour in to the egg mixture, whisking constantly, to temper the eggs. Pour the mixture back into the saucepan and cook over medium-low heat until the temperature reaches 180 F, or the creme is thick enough to coat the back of a spoon and hold a line when you drag your finger through it. Stir in the whiskey.
To serve, scoop the cobbler out onto a plate and pour some anglaise over the top. Best served warm.