Preheat the oven to 400 degrees Fahrenheit. Spray an 8x8 inch baking dish with cooking spray.
Gently combine the peaches, cane sugar, cinnamon, vanilla extract, lemon juice, tablespoon of white rice flour, and salt in a large mixing bowl. Transfer the peach mixture into the prepared baking dish.
Place baking dish onto a rimmed baking sheet and bake for 15 minutes. Carefully remove from oven, stir, and return to oven and bake for 10 minutes more.
While the filling is baking, prepare the biscuits. Combine the white rice flour, almond flour, tapioca starch, cane sugar, baking powder, and salt in a medium bowl. Whisk until ingredients are evenly incorporated.
Add 1 cup almond milk and the olive oil to the dry ingredients. Stir for 2-3 minutes; the mixture should start to thicken. Place bowl in the refrigerator and allow to chill for at least 10 minutes or until ready to top peach filling.
When the peach filling is ready, use ¼ measuring cup to drop 5-8 scoops of biscuit dough on top of filling, using your hands to loosely form dough into a circular shape. This will not completely cover the peach filling.
Using a pastry brush, use the remaining almond milk and brush the tops of the biscuits with it and then sprinkle with sugar.
Bake for 24-26 minutes, or until tops of biscuits start to turn a light golden brown.
Cool peach cobbler for about 20 minutes before serving. Serve warm or at room temperature with vanilla ice cream.