Preheat oven to 375°F. Whisk the flour, sugar, baking powder, and salt in a large bowl. Add butter; using your fingertips, incorporate until only small lumps remain. Gently mix in sour cream and knead until a biscuit-like dough forms.
For the blueberry mixture
Combine the flour, sugar, berries, lemon juice, and lemon zest in a large bowl. Toss to combine. Pour into a medium sized skillet. Tear the biscuit dough into pieces and scatter over berries leaving some of the blueberries exposed.
Transfer the cobbler into the oven and bake until juices are thick and bubbling and topping is cooked through and golden brown, about 45-50 minutes. Let cool for at least 1 hour. Scoop ice cream on top and serve.