In a large bowl or stand mixer, combine the sour cream, sugar, butter, eggs, and vanilla or almond. Beat for 2-3 minutes.
Add the flour, baking powder, baking soda, and salt. Mix just until combined. Dough will be thick and sticky. Divide dough in half and place each half on a large piece of plastic wrap. Press and flatten the dough into a disc, then wrap and cover it with the plastic wrap. Another option is to place the dough between two pieces of parchment or waxed paper, then roll dough out to ¼-inch thick while between the paper. Place dough in the refrigerator to chill for at least 30 minutes.
Preheat oven to 350° F. Line cookie sheets with parchment paper or silicone baking mat.
If not rolled out already, flour the working surface and rolling pin. Roll dough to ¼ inch thick and use cookie cutters to cut out desired shapes. Carefully place cut-out cookie dough on prepared cookie sheets. Repeat with the dough scraps, until dough is used up. Keep other half of dough chilled until ready to use. Be careful not to over-flour, especially as you are rolling out the scraps. The less flour you use, the softer the cookies will be.
Bake one cookie sheet at a time for 8-10 minutes. Edges will be set and middle of cookies will look uniform and set as well, but still be light in color. Let cool on the pan.
In a large bowl with an electric mixer or stand mixer, beat the softened butter, cream cheese, and vanilla for about 3 minutes. Gradually add the powdered sugar, mixing to combine.
Start with 2 tablespoons of the milk or heavy cream and add the salt, beat for about 3 minutes. Add more milk until desired consistency is reached. (3 tablespoons works for me.) I usually use milk because it is easy and convenient for me, but heavy cream will result in a more rich and creamy frosting. For more of a buttercream frosting, replace cream cheese with an additional 1/2 cup butter, for a total of 1 cup butter. Makes 4 cups frosting.
Unfrosted cookies may be frozen up to a month.
These cookies puff up while baking, but will flatten out a little bit while they cool. We don't recommend detailed cookie cutters with this recipe.
Careful not to over-flour while rolling out, otherwise they'll be more dry and less soft.
Use clear vanilla in the frosting, if you want it to be as white as possible. If adding color, use gel food coloring for more vibrant colors.