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For the cream cheese ice cream:
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In a stand mixer or food processor, beat/process the cream cheese until smooth and slightly lightened, around 1-2 minutes on medium-high speed for mixer, and 30 seconds on food processor. Add sour cream, half-and-half, sugar, salt, vanilla extract, and blend until smooth (medium-low speed on mixer).
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Chill thoroughly in the refrigerator for 1-2 hours. Freeze in your ice cream maker according to the manufacturer's instructions.
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For the red velvet cookies:
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Whisk flour, cocoa powder, cornstarch, baking soda, and salt together in a large bowl.
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In a separate large bowl, beat butter and sugar on medium-high speed until light and fluffy. On medium-low speed, mix in egg and vanilla extract. Scrape down the sides of the bowl, and slowly mix in food coloring. Add additional food coloring if needed for desired color.
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On low speed, mix in the flour mixture, half at a time. Refrigerate the dough for at least 1 hour.
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Preheat oven to 350u00b0F. Line cookie sheets with either parchment paper or a silicone mat. Form dough into balls around 2-tablespoons in size (I used a small tablespoon-size ice cream scoop). Place onto the cookie sheets, leaving 2 inches apart between them.
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Bake for 7-9 minutes. Take them out when they're slightly puffed and just set- they will continue to set as they cool. I usually leave the whole pan on the cooling rack for a minute or two, and then take the sheet out and leave the parchment paper or silicone mat on the rack to let them finish cooling.
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Sandwich together and enjoy! You can wrap these individually in plastic wrap and they'll keep well in the freezer for at least a month-probably longer although they didn't last that long here.