Preheat your oven to 325°F and line a baking sheet with parchment paper.
In a large bowl, combine all of your wet ingredients and mix until it's smooth and creamy.
Add your dry ingredients and mix until a thick dough forms with no dry spots left behind.
If the dough is crumbly, add the milk 1 tablespoon at a time until it holds together in a ball when you pinch it, usually 1 to 3 tablespoons total.
Chill the dough for at least 20 minutes so it's easier to scoop and the cookies hold their shape. Use a medium (1.5 tbsp) cookie scoop to portion the dough into 10 balls on your prepared baking sheet.
Lightly flatten each one with your fingers or the back of the scoop since they won't spread a ton in the oven. Bake on 325°F for 8 to 12 minutes, ideally closer to 8 to 9. The edges should look set and the tops just dry, and the centers should still feel soft.
Let the cookies cool on the pan for at least 10 minutes before moving them to a wire rack, then cool them completely before frosting.
While the cookies cool, take out a bowl to mix your frosting.
Add all of the frosting ingredients and mix until it's completely smooth. Set it aside for now.
If the frosting is too thick to spread, loosen it with milk 1 teaspoon at a time and then chill it for 30 minutes to firm up.
Spread about 2 tablespoons of frosting on each cooled cookie. The batch makes around 2 cups, so use 2.5 tablespoon swirls if you want to frost all 12 with nothing leftover.
Store the frosted cookies in an airtight container in the fridge for up to 5 days, and the unfrosted ones keep at room temperature for a few days too. Both freeze well, and the frosted ones thaw in the fridge overnight whenever you want one.