Melt the butter in a small saucepan over medium heat, swirling occasionally. Once it's melted and starts to sputter, whisk constantly until it starts to form brown bits. Reduce the heat to medium-low and continue whisking constantly until it emits a nutty aroma and is chestnut-like in color.
Transfer the browned butter to the bowl of a stand mixer, being sure to include all the brown bits. Let it cool slightly for 10 minutes.
In a medium bowl, whisk together the flour, masa harina, cream of tartar, baking soda, and salt.
To the bowl of browned butter, add the piloncillo and granulated sugar. Fit the mixer with a paddle attachment and mix on medium-high speed for 2-3 minutes.
Add the eggs, egg yolk, and vanilla extract. Mix until well combined then scrape down the bowl.
In two additions, add the flour mixture and mix on low speed until just combined. Scrape down the bowl once more to ensure everything is combined.
Cover the bowl tightly with plastic wrap and chill in the fridge for 1 hour.
Preheat the oven to 400°F (205°C) and line a large baking sheet with parchment paper. Add the rolling sugar and cinnamon to a small, shallow dish and mix to combine.
Use a 3 tbsp cookie scoop to portion the dough and roll the cookies with your hands. Roll in the cinnamon sugar and place about 3 inches (7.6 cm) apart on the prepared baking sheet.
Bake for 10-12 minutes until the cookies are browned along the edges and the tops are cracked. The centers should also look slightly underdone.
Cool on the baking sheet for 5 minutes then transfer to a wire rack to cool completely.