In a medium saucepan, melt 1 cup plus 2 tablespoons of unsalted butter over medium heat. Swirl the pan occasionally, adding a sprig of fresh rosemary, until the butter becomes golden brown and aromatic, about 5-7 minutes. Remove the rosemary once browned and refrigerate the butter until it's solidified, approximately 30-45 minutes.

In a large mixing bowl, beat the chilled brown butter with 1 1/3 cups of granulated sugar for about 2 minutes until well-combined and creamy. Add in the large egg, egg yolk, and 1 teaspoon of vanilla extract, mixing for another minute.

In a separate bowl, sift together 2 1/2 cups of all-purpose flour, 1 teaspoon of baking soda, 1/2 teaspoon of baking powder, 1/4 teaspoon of salt, and 2 teaspoons of chopped fresh rosemary. Gradually incorporate the dry mixture into the wet ingredients, stirring until just combined.

Using a 1 1/4-ounce scoop, scoop the dough onto a parchment-lined cookie sheet, keeping them spaced out. Refrigerate the dough for at least 30 minutes.

While the dough chills, mix 1/2 cup of granulated sugar with the zest of one lemon in a small bowl. Use your fingers to rub the zest into the sugar.

Preheat your oven to 350°F (175°C). Once the dough is chilled, roll each cookie ball in the lemon sugar, then place them 2 inches apart on a parchment-lined baking sheet. Bake for approximately 12 minutes.