Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a large mixing bowl, use an electric mixer to beat the softened butter and sugar together until light and fluffy.
Mix in the egg and vanilla extract, blending until smooth.
In a separate bowl, whisk together the all-purpose flour, baking soda, and salt.
Gradually add the dry ingredients to the butter mixture, stirring until combined. The dough should be soft but not sticky.
Roll the dough into 1-inch balls and place them on the prepared baking sheet, spacing them about 2 inches apart. Gently flatten each ball with the bottom of a glass or your fingers.
Bake for 8-10 minutes, or until the edges are lightly golden. Be careful not to overbake, as the cookies will continue to firm up as they cool.
Let the cookies cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely.