Preheat your oven to 350°F (175°C) and line two baking sheets with parchment paper to prevent the cookies from sticking and to allow for easy cleanup.
In a medium bowl, whisk together the all-purpose flour, salt, baking powder, and baking soda until evenly combined. Set this dry mixture aside for later.
In the bowl of a stand mixer using the paddle attachment, or with a handheld mixer, beat 1 cup of softened butter and 1 cup of granulated sugar together until the mixture is light and fluffy. This helps incorporate air, giving your cookies a tender texture.
Add the egg and 2 teaspoons of vanilla extract to the creamed butter and sugar mixture. Beat until everything is well combined and the mixture appears lighter in color.
Gradually mix the dry ingredients from Step 2 into the wet mixture from Step 4. Stir until just combined and a soft dough forms—be careful not to over-mix, as this can make the cookies tough.
Using a cookie scoop or spoon, portion out 1.5 tablespoon-sized balls of dough and place them on the prepared baking sheets, leaving at least 4-5 inches between each ball to allow for spreading. Bake one tray at a time in the preheated oven for 8-11 minutes, until the edges are set but the centers are still soft. Let the cookies cool on the trays for 10 minutes, then transfer to a wire rack to cool completely.
While the cookies cool, make the buttercream frosting. In a medium bowl, combine 3/4 cup softened butter, 1 1/2 cups powdered sugar (sifted for smoothness), 1/2 teaspoon vanilla extract, and 1/8 teaspoon salt. Beat the mixture until smooth and creamy, adding more powdered sugar if you prefer a thicker consistency. I like to make sure the butter is really soft for an extra silky frosting.
Once the cookies have cooled completely, generously spread the buttercream frosting from Step 7 over each cookie. Enjoy your freshly frosted cookies!