To prepare the ice cream, first line a sheet pan with parchment paper. Remove the ice cream from the freezer and let it sit at room temperature for about 5 minutes. Scoop the ice cream into a bowl of a stand mixer and whip until soft, but not melted. Fold the frozen strawberry slices into the mixture by hand. Pour the mixture onto the prepared baking sheet and spread to a 1/2'' thickness. Cover the ice cream with another piece of parchment paper, and then place the sheet pan in the freezer.
When the ice cream has hardened, remove the sheet pan from the freezer. Dip a round cookie cutter in hot water, then make ice cream cutouts. Place the cutouts back into the freezer until needed.
To prepare the cookies, preheat the oven to 350°F. Line three cookie sheets with parchment paper. Set aside. Combine the flour, baking soda, and salt in a medium-size bowl. Set aside. Then combine the buttermilk, lemon juice, and vanilla into a small bowl. Set aside.
Fit a stand mixer with a paddle attachment, and (on medium speed) combine the butter and sugar until it's pale and fluffy. Add the eggs and mix until well-blended. Add the flour and buttermilk mixtures alternately, on low speed. Make sure to begin and end with the flour mixture. Mix until well-blended.
Spoon 2 Tbsp of batter (about 2'' apart) onto the prepared cookie sheets. Bake for 12–14 minutes. Place the cookies on a cooling rack so they can cool completely.
To prepare the topping, fit a stand mixer with a whisk attachment, and combine the whipped topping, marshmallow fluff, and strawberry syrup. On medium speed, whip for 2–3 minutes until light and fluffy. Refrigerate the marshmallow topping until needed.
To assemble the sandwiches, evenly spread the marshmallow topping on the flat side of two cookies. Place a pre-cut ice cream circle on top of one of the cookies and then top with the other cookie. Freeze until ready to eat.
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