Brown Butter Crinkle Cake

Preheat oven to 350 degrees F (175 degrees C). Line the bottom of a 9x13-inch baking pan with parchment paper, leaving an overhang on two sides for easy removal. (5 minutes)

To make the browned butter, melt butter in a light-colored saucepan over medium heat. Continue cooking, swirling the pan occasionally, until the butter is browned, fragrant, and has nutty brown bits at the bottom. This should take about 5 to 10 minutes. Immediately pour into a heatproof bowl to prevent further cooking and let cool slightly.

For the syrup, combine sugar, water, lemon juice, and cinnamon stick in a small saucepan. Bring to a boil over medium heat, stirring until sugar is dissolved. Reduce heat to low and simmer for 10 minutes, or until slightly thickened. Remove from heat and let cool completely. (15 minutes)

While the syrup cools, gently unroll the thawed phyllo dough. Stack two sheets of phyllo together. Starting from a short end, fold the sheets accordion-style into a strip, making approximately 1 1/2-inch folds. Arrange the folded phyllo along one short end of the prepared pan. (10 minutes)

Repeat the stacking and folding process with the remaining phyllo, evenly spacing the strips in the pan to create a crinkled effect. Bake in the preheated oven for 10 minutes to begin setting the phyllo.

Remove the pan from the oven. Drizzle the cooled brown butter evenly over the baked phyllo, ensuring it seeps into the folds. Return to the oven and bake for another 10 minutes to further crisp the phyllo.

In a separate bowl, whisk together milk, eggs, vanilla extract, and salt until well combined. Carefully pour this mixture evenly over the partially baked phyllo, ensuring all areas are covered. Bake for 35 to 40 minutes, or until the custard is set and the top is golden brown.

Remove the cake from the oven and let it cool slightly. While still warm, pour the cooled syrup evenly over the top (remove the cinnamon stick). Let the cake cool on a wire rack for at least 15 minutes before cutting into 20 squares and serving warm.