Preheat the oven to 400 degrees. Make the Filling: Whisk sugar, cardamom, allspice, cornstarch and salt together in a medium bowl. Add peaches, vanilla extract and lemon juice and gently toss until the peaches are evenly coated. Transfer the fruit to a 9 inch deep dish pie plate and bake until fruit begins to release liquid, about 20 minutes.
Meanwhile, make the Biscuit Topping: Combine the flour, sugar, baking powder, baking soda and salt together in the work bowl of a food processor. Pulse until combined. Scatter cubes of butter over the top and pulse until the mixture resembles wet sand with a few pea-sized pieces of butter, about 8-10 pulses. Transfer the mixture to a large bowl. Add skyr or yogurt and 2 tablespoons water. Mix together using a fork and/or your fingers until a dough forms, adding another teaspoon or two of water if necessary to help the dough come together.
Once the fruit is out of the oven, use an ice cream scoop or large spoon to drop 6 equal-sized mounds of dough on top of the hot peach mixture leaving at least a half inch between each biscuit. Sprinkle the dough mounds and peaches wth turbinado sugar and transfer to the oven. Bake until the filling is bubbly and biscuits are golden brown, about 20 minutes. Transfer to a wire rack to cool. Serve warm with vanilla ice cream or whipped cream.
Notes
*The easiest way to peel peaches is to use a serrated peeler. If you don’t have a serrated peeler, you can use a paring knife to score each peach with an “X” at the base and blanch the peaches in a pot of simmering water for 20-30 seconds. Remove the peaches from the simmering water and immediately transfer to a bowl of ice water. This blanching and shocking process will loosen the skins and you should be able to peel them easily by hand beginning where you made the “X”.