For the filling:
4 medium peaches, unpeeled, sliced into 1/4-inch wedges
1/2 cup (3 1/2 ounces) granulated sugar
2 tablespoons cornstarch
2 teaspoons freshly grated ginger (or to taste)
1 teaspoon vanilla bean paste or pure vanilla extract
1/4 teaspoon kosher salt
1/8 teaspoon almond extract
For the crust:
1 1/2 cups (7 ounces) all-purpose flour
3/4 cup (3 ounces) powdered sugar
1/2 teaspoon kosher salt
6 ounces (12 tablespoons) chilled unsalted butter, cut into 12 pieces (1 tablespoon each)
1 teaspoon vanilla bean paste or pure vanilla extract
For the biscuit topping:
3/4 cup (3 1/2 ounces) all-purpose flour
2 tablespoons granulated sugar
1 teaspoon baking powder
1/2 teaspoon kosher salt
2 tablespoons chilled unsalted butter, cubed
1 teaspoon vanilla bean paste or pure vanilla extract
1/3 cup whole or 2% milk
For the filling, combine the peaches, sugar, cornstarch, ginger, vanilla bean paste, salt, and almond extract in a large bowl. Set aside.
For the crust, preheat the oven to 350°F. Combine flour, confectioners sugar, and salt in the bowl a food processor and pulse to combine. Add the butter and vanilla and continue pulsing until the dough begins to form small clumps, about 1 minute. Transfer the mixture to an 8x11 or 9x9 baking dish and press into a smooth, even layer. Transfer pan to freezer for 5 to 10 minutes.
Meanwhile, make the biscuit topping. Combine flour, sugar, baking powder, salt, butter, and vanilla bean paste in the food processor (no need to clean it) and pulse until the butter has formed large crumbs. Transfer to a mixing bowl and stir in milk until a soft, sticky dough has formed.
When ready to bake the bars, remove the baking dish from the freezer and spread the peach filling evenly over the dough. Drop tablespoon-sized dollops of the biscuit topping over the peach mixture. Bake for one hour, until the topping is light golden-brown and the filling has set. Cool completely before slicing into squares. Serve with vanilla bean ice cream, if desired.