In a large bowl, whisk the flour with the salt, pepper, baking powder and baking soda until evenly combined. In the bowl of a stand mixer fitted with the paddle, beat the butter and sugar at medium speed until light and fluffy, about 3 minutes. Beat in the eggs one at a time until incorporated. Add the dry ingredients and beat at low speed until just combined. (Make ahead: The dough can be stored in the refrigerator for up to 3 days.)
Preheat the oven to 375°F. Scoop 1” round balls onto a cookie sheet lined with a Tovolo Silicone Baking Mat – be sure to arrange at least 3 inches apart. Bake the cookies for 12 to 14 minutes, until set at the edges and lightly browned; rotate the baking sheets from top to bottom and front to back halfway through baking. Let the cookies cool for 10 minutes, and then transfer to a rack to cool completely.