Preheat your oven to 375°F (190°C). In a mixing bowl, cream together the butter, granulated sugar, brown sugar, and corn syrup for about 3 minutes until light and fluffy. Beat in the egg, vanilla extract, and almond extract until combined.

In a separate bowl, whisk together flour, baking powder, baking soda, and salt, then gradually incorporate them into the wet mixture until a soft dough forms.

Using a cookie scoop, portion out the dough into uniform balls (about 1.5 inches in diameter). Place them on parchment-lined baking sheets, spaced two inches apart. Flatten the tops slightly with your palm.

Bake the cookies for 10-12 minutes, monitoring closely. Remove from the oven and allow to cool completely on wire racks.

Thaw the peach ice cream for 10 minutes. Combine it with frozen peaches and whipping cream in a mixing bowl, blending until smooth. Line a baking pan with wax paper and spread the mixture into it. Freeze for at least 3 hours.

Cut circles from the frozen ice cream using a cookie cutter. Place one circle between two cookies to form a sandwich.

Wrap each sandwich in wax paper, then cover with aluminum foil. Store them in the freezer for up to three months.