In a saucepan, melt unsalted butter over medium heat, swirling until it foams. Add rosemary sprig and cook for 5-7 minutes until golden brown. Refrigerate for 30-45 mins.

In a mixing bowl, beat the chilled brown butter and granulated sugar for 2 minutes. Add egg, yolk, and vanilla. Beat for another minute.

In another bowl, sift flour, baking soda, baking powder, and salt. Stir in chopped rosemary. Gradually mix with the butter mixture.

Scoop 1 1/4 oz portions onto a lined cookie sheet, cover, and chill for 30 minutes.

Combine lemon zest and granulated sugar in a small bowl, rubbing the zest into the sugar.

Preheat oven to 350°F (175°C). Roll each cookie in the lemon sugar and place on parchment-lined sheets. Bake for 12 minutes until edges are golden and centers are puffy.