Combine 1/2 cup of butter and 1/2 cup of granulated sugar and brown sugar in the bowl of a stand mixer fitted with the paddle attachment. Beat on low for a minute, then increase the speed to medium and beat until light and fluffy, about 2-3 minutes. Scrape down the sides of the bowl.
Add the 1 egg and 2 teaspoons vanilla extract and continue beating until fully combined.
In a separate bowl combine the 1 cup flour, 2/3 cup cocoa powder, 1 teaspoon baking soda, 1 teaspoon cinnamon, 1/4 teaspoon salt, and 1/4 teaspoon cayenne pepper. Whisk to break up any lumps.
Add the flour mixture to the mixer and beat on low until combined. Cover the bowl with plastic wrap and refrigerate for at least an hour but up to overnight.
Heat oven to 350°F. Line two large baking sheets with parchment paper. Pour turbinado sugar into a small bowl.
Let cookie dough sit out for 10-15 minutes if it has been sitting in the fridge for more than an hour. Scoop dough into 1-2 tablespoon-sized balls. A cookie scoop makes this easy. Roll the balls in the sugar to coat and place 2-inches apart on the baking sheets. Press down gently to slightly flatten each ball. Sprinkle a little more turbinado sugar on top of each one if necessary to get a good coating.
Bake for 10-12 minutes or until the edges appear set but the middle is still soft. Let cool on the baking sheet for 5 minutes. Then let cool completely on a wire rack.