Combine the butter with the sugar and the brown sugar in a mixing bowl. Beat on medium speed until light and fluffy, about 4 to 5 minutes.
Add the egg and blend into the butter and sugars.
Whisk together the flour and kosher salt and stir into the butter and sugar mixture, blending in on low speed.
Toss in the chopped pecans and pour in the vanilla extract. Blend using low speed just until mixed together.
Using a very small ice cream scoop or teaspoon, drop small rounds of dough, about 1” in diameter, onto baking sheets lined with a Silpat liner or parchment paper.
Leave about 3” of room between the cookies, they spread as they bake.
Bake in a 350-degree oven for about 10 to 12 minutes, or until the cookies are just golden on the edge and no longer wet in the center.