Preheat the oven to 400°F with a rack in the center position.
In a large bowl combine the peaches, ¾ cup of the sugar, cornstarch, vanilla extract, and almond extract. Transfer the peaches to a 9x13-inch baking dish and spread out in a single layer.
Bake the peaches for 10 minutes.
While the peaches are baking, make the biscuits. In a food processor, pulse the flour, baking powder, salt, and remaining ½ cup sugar 5 times until the ingredients are mixed. Add the butter and pulse until the largest pieces of butter are smaller than grains of rice, about 10 more times. Pour in the cream and pulse just until the dough gathers in clumps.
Turn the dough out onto a piece of parchment paper and divide it into 12 equal pieces. Lightly form each piece into a shaggy disk the size of a sausage patty, about 2½ inches in diameter.
In a small bowl, whisk together the egg and heavy cream. Arrange the biscuits on top of the hot peaches, brush with egg wash, and sprinkle with turbinado sugar. Transfer the baking dish back in the oven and bake for another 20-25 minutes until the biscuits are golden brown.
Serve the cobbler warm with vanilla ice cream, sweetened crème fraîche, or fresh whipped cream.