Preheat the oven to 375°F. Line two baking sheets with parchment paper.
To make the dough: In the bowl of a stand mixer fitted with the paddle attachment, add the butter, cane sugar, and vanilla extract. Mix on low until combined and there are no butter chunks.
Add the sourdough discard, milk, and cream cheese. Then add the flour, cocoa powder, beet powder, baking powder, and sea salt in that order. Mix on low until combined into a smooth cookie dough.
Using your hands, or a cookie scoop, form the dough into 12 balls and place on the prepared baking sheets. Flatten them so they are about 2 1/4-inches in diameter. Space evenly apart, you’ll have 6 cookies per sheet.
Bake for 15 to 17 minutes or until the tops look cracked and the edges look dry. Round them out with a cookie cutter after baking for perfectly round cookies (see video). Allow the cookies to cool completely on the baking sheets before frosting.
To make the frosting: In the bowl of a stand mixer fitted with the paddle attachment, add the butter, cream cheese, powdered sugar, and vanilla extract. Mix on low until combined, then speed mixer up to high and whip for 2 to 3 minutes or until it’s light and fluffy. Be sure to scrape down the sides of the bowl part way through to ensure everything is combined.
Reserve a small amount of frosting (a few tablespoons) in three small bowls for the decorating frosting. Transfer the remaining frosting to a piping bag with Ateco tip #808.
Pipe dollops of frosting onto each cookie. Then turn the cookies upside down and smash them against the parchment paper. Place the tray in the freezer to set the frosting. This will take about 30 minutes, the cookies should remove from the parchment paper easily without sticking.
Add the beet powder, strawberry powder, and raspberry powder to each of the 3 bowls reserved with frosting. You can add less for more pastel colors or more for brighter colors. Mix it up. If the frosting seems dry, add a few drops of water. If you add more color, you’ll need a bit more water to make it smooth.
Transfer the colored frosting to piping bags with Ateco tips #4, 6, and 30. I used #30 for raspberry, #6 for beet, and #4 for strawberry, but you can do it however you like.
Pipe hearts, XOXO, or other Valentine’s Day decorations on the cookies. Do this however you like!
Be sure to store cookies in an airtight container in the fridge.