Put ice cream, peaches, and whipping cream into a Vitamix blender or one similar.
Line a quarter sheet baking pan with parchment or wax paper. Add the peach ice cream and smooth it out level with a spatula. Freeze this pan for at least 3 hours or overnight.
Preheat oven to 375. Line two baking sheets with parchment. You could also spray them with non-stick cooking spray if you prefer.
Place room temperature butter, brown and white sugar, butter, corn syrup, vanilla, almond extract, and egg in a large mixing bowl. Beat with an electric mixer until well blended. Add in flour, baking powder, baking soda, salt and beat until well blended.
Using a 1 1/2 inch cookie scoop, drop cookie dough balls on the prepared baking sheets, about two inches apart.
Bake cookies for ten minutes until the edges are just barely beginning to brown, they'll look soft. If you bake these cookies too long, they'll be crunchy rather than chewy.
Remove from oven and cool on baking sheet for 5 minutes, then transfer to rack to cool completely.
Assemble Ice Cream Sandwihes
To ensure a clean-cut, rinse the cutter with cold water. Do this each time before you cut the ice cream.
After pressing down your cookie cutter, put your free hand underneath the wax paper and push up from the bottom to e sure you have a clean cut. Put the cutter on the bottom of one of the cookies. Using a spoon, push the ice cream out of the cutter onto the cookie bottom.
Place the other cookie on top to make the homemade ice cream sandwich.
Wrap each sandwich in a square of wax paper. Then wrap it again in a square of foil. Freeze for up to a month