Cut 1 stick (8 tablespoons) of the butter into small cubes and keep chilled. Melt the remaining stick in a light-colored saucepan over medium heat, stirring, until the milk solids turn deep golden and smell nutty, 3 to 5 minutes. Scrape the browned butter into a large mixing bowl, then immediately stir in the cold butter cubes until mostly melted. Let cool until opaque and just slightly warm, 10 minutes.
In a separate bowl, whisk together the flour, baking soda, fine sea salt, cinnamon, and espresso powder. Tip: For best texture, weigh your flour or lightly spoon it into the cup and level.
Add the granulated sugar and brown sugar to the cooled butter. Beat with a hand mixer on medium-high until lightened and creamy, 2 to 3 minutes.
Beat in the egg, egg yolk, and vanilla until the mixture is glossy and smooth, 30 to 45 seconds, scraping down the bowl once.
Add the dry ingredients in two additions, mixing on low just until no dry streaks remain. Let the dough stand 10 minutes at room temperature to hydrate, then cover and chill until scoopable but not firm, 30 to 45 minutes.
Preheat the oven to 360°F (182°C). Line two baking sheets with parchment paper.
Using a 3-tablespoon scoop (about 1 1/2 ounces), portion dough into mounds and arrange 2 1/2 inches apart on the prepared sheets. Roll each portion quickly between your palms for even rounds if you like.
Bake one sheet at a time for 12 to 13 minutes, until the edges are set and lightly browned while centers look slightly soft. At minute 8, rap the pan once against the oven rack and rotate for even baking to encourage a chubby, chewy center.
Cool on the sheet for 5 minutes, then transfer cookies to a rack to finish cooling 10 minutes before serving.