Preheat oven to 375°F (190°C). In a medium saucepan, combine melted butter, 1 cup sugar, water, vanilla, cinnamon, and nutmeg. Bring to a simmer over medium heat, stirring until sugar dissolves. Remove from heat and stir in diced peaches. Pour the mixture into a 9x9 inch glass baking dish, spreading peaches evenly.

In a large bowl, whisk together flour, baking powder, 1/4 cup sugar, and salt. Cut in cold butter using a pastry cutter or your fingers until mixture resembles coarse crumbs with pea-sized butter pieces. Gradually add cold buttermilk, stirring just until dough comes together (do not overmix).

Turn dough out onto a lightly floured surface. Pat into a 1-inch thick rectangle (about 8x8 inches). Cut into 9 equal squares. Place biscuit squares evenly over the peach syrup in the baking dish—they will be close together. Bake for 25-30 minutes until biscuits are golden brown and syrup is bubbling around edges.

While biscuits bake, whisk together powdered sugar, 2 tablespoons milk, vanilla, and salt until smooth. Add more milk if needed for drizzling consistency. When biscuits are done, let cool in pan for 5 minutes. Drizzle icing generously over warm biscuits. Serve directly from the baking dish.