Using a standing mixer, beat 1 cup room temperature butter with 3/4 cup sugar really well, so it becomes fluffy and pale in color.
Add an egg and 1 tsp vanilla extract and mix until combined and smooth consistency.
Mix dry ingredients (3 cups flour, 1 tsp baking powder, and 1/4 tsp salt) together in a separate bowl, then add to the wet ingredients in two batches. Mix everything until well combined but don’t overmix it.
When done, you can lightly knead the dough, making a ball, wrap in a plastic wrap and refrigerate from 1-2 hours to overnight.
When you roll out the dough it might be a bit sticky. You can use a little bit of flour to prevent it from sticking to a roller or a counter. However, I have a different trick that always helps me. Put the dough between two sheets of parchment paper, then roll over the parchment paper about 1/4-inch thick.
After you cut out the cookies and put them on the baking sheet, put the sheet with the cookies back in the fridge for 10 minutes to chill.
Bake the cookies at 350°F for 9-10 minutes until the bottom gets a very light golden color.
Note: The measurements for the frosting will vary, based on the amount of liquid you use and the desired thickness of the icing.