Place butter in a medium saucepan over medium heat. Stir constantly as it melts, foams, and the milk solids begin to brown. Once it smells nutty and the solids are golden brown (not black!), immediately remove from heat and transfer to a heatproof bowl, and allow to come to room temperature.

Weigh out ¾ cup of the brown butter into a large bowl. If you're short a few grams, add regular unsalted butter to make up the difference. Place in the freezer for about 30 minutes, until solid yet soft (like the consistency of softened butter). You want it firm enough to cream, but not rock-hard.

Add the molasses and beat until thoroughly combined, about 30 seconds.

Add the egg and vanilla extract and beat until combined, about 1 minute. Scrape down the sides and bottom of the bowl as needed.

On low speed, slowly mix the dry ingredients into the wet ingredients until just combined. The cookie dough will be slightly sticky. Cover the dough tightly with aluminum foil or plastic wrap and chill for at least 2-3 hours (the brown butter dough benefits from longer chilling, as it's softer). Dough can be chilled up to 2–3 days.

Preheat oven to 350°F. Line two large baking sheets with parchment paper or silicone baking mats. Remove cookie dough from the refrigerator. If the cookie dough is chilled for longer than 3 hours, let it sit at room temperature for 15-20 minutes to make it easier to scoop. Roll the cookie dough into 1-tablespoon balls.

Roll each cookie in granulated sugar and arrange 3 inches apart on the baking sheets.

Bake for 11–12 minutes or until edges appear set. If the tops aren't appearing cracked, remove the baking sheet from the oven and gently tap it on the counter 2–3 times. This will help those warm cookies spread out and crack on top. Return to the oven for 1 additional minute. Remove the cookies from the oven and let them cool on the baking sheet for 5 minutes, then transfer them to a wire rack to cool completely.