Preheat oven to 350 degrees F. Spray a 13- by 9-inch metal baking pan with cooking spray, then line with parchment paper, with parchment paper edges hanging over the side.
Melt the butter in a large skillet set over medium heat. Continue to cook, stirring constantly, until the butter turns golden brown. Remove from heat. Cool to room temperature.
In a medium bowl, whisk together flour, baking soda, salt and cinnamon. Set aside.
In a small bowl, combine eggs, espresso powder and vanilla extract. Whisk until espresso powder is dissolved. Set aside.
In the bowl of a stand mixer (or a large bowl, using a hand mixer), combine brown sugar, granulated sugar and cooled brown butter. Beat on medium speed until well-combined, about 3 minutes.
Add the egg mixture and beat again, about 30 seconds.
With the mixer set to low speed, gradually add the flour mixture. Scrape down the sides as necessary and beat just until the flour is combined.
Remove the bowl from mixer and stir in the white chocolate chips.
Gently press the mixture into the pan until even.
Bake until the top is medium golden brown, 20 to 25 minutes. Remove from oven and cool on a wire rack for 15 minutes.
Holding the parchment paper flaps, lift the bars out of the pan and let cool completely.
Cut into bars and serve.