In a medium saucepan over medium heat, melt 1 cup and 2 tablespoons of unsalted butter, add a sprig of rosemary and cook until it turns deep golden brown, about 5-7 minutes. Remove rosemary and let cool for 30-45 minutes in the refrigerator.

In a large mixing bowl, combine the cooled brown butter with 1 ⅓ cups of granulated sugar and beat for 2 minutes until light and fluffy. Then add in one large egg, one egg yolk, and 1 teaspoon of vanilla extract, beating for an additional minute.

In a separate bowl, sift together 2 ½ cups of all-purpose flour, 1 teaspoon of baking soda, ½ teaspoon of baking powder, and ¼ teaspoon of salt. Stir in 2 teaspoons of chopped fresh rosemary. Gradually add this to the wet ingredients until just combined.

Using a 1 ¼ oz ice cream scoop, portion the dough onto a parchment-lined cookie sheet, cover with plastic wrap, and refrigerate for at least 30 minutes.

In a small bowl, mix together the zest of one lemon with ½ cup of white granulated sugar. Rub the lemon zest into the sugar until fragrant. Set aside.

Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper. Roll each dough ball in the lemon sugar and arrange them on the sheet about 2 inches apart. Bake for 12 minutes until edges are lightly golden. Cool completely on a wire rack.