Preheat oven to 450F degrees (yes, that is the correct temperature). Spray a 9x9-inch oven safe glass or ceramic baking dish with nonstick cooking spray.
In a medium bowl, mix together the flour, sugar and baking powder.
Pour in the heavy cream and one teaspoon of the vanilla extract. Stir until a sticky dough forms. If batter still looks dry, add a tad bit more of the heavy cream until you have a sticky dough.
Gently stir in diced peaches.
In a microwave-safe bowl melt stick of butter in the microwave (or melt right in the baking dish you'll be using as long as it's not metal). Pour melted butter into prepared baking dish.
Pour biscuit dough into baking dish (right on top of the melted butter.) Some of the butter will run over the top of the dough. Spread out the batter evenly (as best as you can). I find this is easiest if I spray my hand with nonstick spray and then gently push the batter around.
Cut the dough into 9 squares. This doesn’t need to be perfect. It will just help with cutting the finished biscuits later.
Bake (on the middle oven rack) for about 30-35 minutes, rotating dish once during baking. At this point, I will usually take out the biscuits and tent the baking dish with foil to prevent them from over-browning. Oven times DO VARY but biscuits should be golden brown and when you insert a toothpick in the center, it should come out clean with no wet batter.
In a bowl, whisk together powdered sugar with milk and ½ teaspoon of vanilla extract. Drizzle on top of the warm biscuits.
Allow the biscuits to cool slightly then slice and serve.
