The ice cream takes at least 6 hours to stiffen. It’s a good idea to make the ice cream the night before you plan to enjoy the ice cream sandwich cookies. Pour whipping cream into the bowl of a stand mixer with paddle attachment or a medium bowl that you’ll whip with an electric hand mixer. Whip the cream in a bowl until soft peaks form.
Transfer the whipped cream to a medium bowl. Some cream might still be in the bowl you used for whipping, but no need to wash it. You will add the whipped cream back to the bowl again soon.
Add the softened cream cheese and sweetened condensed milk to the first bowl and beat until smooth. Then, gently fold in the whipped cream with a spatula. Mix gently to retain the air you created when whipping the cream.
Transfer mixture to a freezable container. Be sure your container has extra room to mix in the strawberry jam and to allow the ice cream to expand when it freezes. Open the jam jar and use a butter knife to stir the jam and loosen any clumps. Drizzle the strawberry mixture on top and swirl with a knife. Cover and freeze for 6 hours or until firm.
Position oven racks so the oven is divided in thirds. Preheat oven to 400°F. Place one sheet of parchment paper on each baking sheet.
Using a stand mixer with paddle attachment or an electric hand mixer and medium bowl, cream softened butter and Bag A at medium high speed thoroughly until light and fluffy. Then add the eggs and mix thoroughly.
Reduce your mixer speed to low, and add Bag B. Mix until just combined. Then, place dough in your refrigerator for at least 15 minutes. Don’t skip this step! Without refrigeration, your cookies will spread too much when they bake.
Pour Bag C into a small bowl. Pull your bowl of cookie dough out of the refrigerator and, using a flatware teaspoon, scoop out rounded teaspoon of dough. Use hands to roll into a ball. Roll half of the dough balls in the cinnamon sugar mix. The other half don’t need to be rolled in the mix. Use fingers to flatten balls slightly to about a half inch thick. Space each ball 2 inches apart. For most baking sheets this means no more than 8 balls per sheet.
Place cookie sheets on top and bottom rack. Bake 8-10 minutes, or until slightly golden, switch cookies from top rack to bottom rack and vice versa half way through. They will puff up at first, then flatten out. To avoid a melty, messy situation, allow cookies to cool completely before assembling cookie sandwiches. To assemble, remove ice cream from the freezer. It may need to sit out for a few minutes to soften. Take one cookie without cinnamon sugar (bottom) and one with it (top). Use your ice cream scoop to place one round scoop of ice cream on the bottom cookie and flatten slightly with the top cookie. Enjoy!