In a medium saucepan, melt the unsalted butter over medium heat, stirring frequently. After about 5 minutes, add the fresh rosemary and continue cooking until the butter turns a deep golden brown and releases a nutty aroma, about 2 more minutes. Remove the rosemary, transfer the brown butter to a bowl, and chill in the refrigerator for 30–45 minutes until solidified.

Once the brown butter is chilled, beat it in a mixing bowl with white granulated sugar for about 2 minutes until the mixture is fluffy. Then, add the large egg, egg yolk, and vanilla extract, mixing for another minute to incorporate everything well.

In a separate bowl, sift together all-purpose flour, baking soda, baking powder, and salt. Stir in the chopped fresh rosemary, ensuring even distribution. Gradually combine the dry mixture with the wet ingredients, mixing until just combined.

Utilizing a 1 1/4 oz ice cream scoop, portion the dough onto a parchment-lined baking sheet, spacing them evenly apart. After scooping all the dough, refrigerate the sheet for at least 30 minutes.

While the cookie dough chills, make the lemon sugar by mixing the zest of one lemon with white granulated sugar in a small bowl.

Preheat your oven to 350°F (175°C). Once the dough is chilled, roll each cookie between your hands, coating them generously in the lemon sugar. Place on a baking sheet 2 inches apart and bake for 12 minutes, or until golden brown.