Heat the oven to 350° F. In the bowl of a standing mixer fitted with the paddle attachment, or using a hand blender, cream together the butter and peanut butter. Beat in the two sugars until light, about 3 minutes.

Beat in the egg and vanilla, scraping down the sides of the bowl once to make sure they're evenly incorporated. Add the salt, baking soda and flour and beat just until combined.

Give the dough one last fold with a spatula. You can chill the dough and then roll it into balls (about ¾-inch in diameter), or arrange heaping teaspoonfuls of the soft dough directly on parchment-lined baking sheets, spaced 2 inches apart. Use the back of a fork dipped in flour to gently flatten each cookie and make a crosshatch pattern.

Bake the cookies for about 10 minutes, until lightly golden and just firm around the edges. Let them cool on the baking sheets for a few minutes, then transfer to a baking rack to cool completely.

These will keep in an airtight container for several days, but they are best while fresh!