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Preheat the oven to 325°F. Line 2 baking sheets with parchment paper.
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In the bowl of a stand mixer, cream the butter, peanut butter, and sugars for 3 minutes on high speed. Add the eggs and vanilla and combine, scraping down the sides of the bowl.
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In a medium bowl, sift together the salt, baking soda, flours, and cocoa powder.
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Mix the dry ingredients into the butter mixture and fold in the chocolate chips. Scoop a heaping tablespoonful of dough at a time and place 2 inches apart on the prepared baking sheets. Gently press down on the mounds to create a flat top, sprinkle with fleur de sel, then bake until the cookie tops just start to crack, 15 to 18 minutes.