Preheat an oven to 350 degrees F (175 degrees C). Whisk the flour and baking powder together in a small bowl; set aside.
Stir the brown sugar, 1/4 cup melted butter, and amaretto liqueur in a 9-inch pie pan until the sugar has dissolved. Arrange the peach slices in the pan and sprinkle with the pecans; set aside. Beat 1/4 cup butter and the white sugar with an electric mixer in a large bowl until light and fluffy. Beat in the first egg until incorporated, the beat in the second along with the almond extract. Pour in the flour mixture alternately with the milk, mixing until just incorporated. Gently pour the batter over the peaches and pecans.
Bake in the preheated oven until a toothpick inserted into the center comes out clean and the cake is golden brown, about 25 minutes. Cool in the pan for 10 minutes before running a knife along the edges and inverting onto a serving plate to cool.