Preheat oven to 375°F (190°C). Lightly grease an 8x8 inch baking dish.

Prepare the filling: In a large bowl, gently toss the halved apricots with granulated sugar, water, lemon juice, flour, and almond extract until evenly coated.

Pour the apricot mixture into the prepared baking dish, spreading them into an even layer.

Prepare the topping: In a separate medium bowl, whisk together the flour, baker's sugar, baking powder, and salt.

Cut in the cold butter using a pastry blender or your fingertips until the mixture resembles coarse crumbs. Stir in the milk until just combined; do not overmix.

Spoon the cobbler topping over the apricot filling in dollops, leaving small gaps between the mounds of dough. The topping will expand during baking.

Bake for 40 to 45 minutes, or until the topping is golden brown and the fruit filling is bubbly around the edges.

Let the cobbler cool for at least 15 minutes before serving warm, ideally with vanilla ice cream or whipped cream.