Start by melting 1 cup plus 2 tablespoons of unsalted butter in a medium saucepan over medium heat. Stir constantly for about 5–7 minutes until it turns golden brown and releases a nutty aroma. As it cooks, add a sprig of fresh rosemary to infuse the butter with flavor. Once browned, remove the rosemary and let the butter cool for 30–45 minutes.

In a large mixing bowl, combine the chilled brown butter with 1 and 1/3 cups of granulated sugar. Using a hand mixer, beat on medium speed for about 2 minutes until well combined. Next, add in 1 large egg, 1 egg yolk, and 1 teaspoon of vanilla extract, beating for an additional minute until the mixture is smooth and creamy.

In a separate bowl, sift together 2 and 1/2 cups of all-purpose flour, 1 teaspoon of baking soda, 1/2 teaspoon of baking powder, and 1/4 teaspoon of salt. Stir in 2 teaspoons of chopped fresh rosemary to distribute the herb evenly. Gradually mix the dry mixture into the wet ingredients, stirring just until combined to avoid overmixing.

Using a 1 and 1/4 oz ice cream scoop, portion out the cookie dough onto a parchment-lined baking sheet. Leave space between each scoop to allow for spreading. Cover the dough with plastic wrap and refrigerate for at least 30 minutes, helping the Rosemary Cookies with Lemon Sugar maintain their shape during baking.

In a small bowl, combine 1/2 cup of granulated sugar with 2 teaspoons of lemon zest. Use your fingers to rub the zest into the sugar; this will release the lemon oils, creating a fragrant coating. Set this lemon sugar aside to roll the cookie dough balls in before baking.

Preheat your oven to 350°F (175°C). Take the chilled cookie dough balls and roll each one in the prepared lemon sugar to coat thoroughly. Place them onto a parchment-lined baking sheet, leaving ample space between each cookie. Bake for approximately 12 minutes, or until the edges are golden brown and the centers appear puffy.

Once baked, remove the Rosemary Cookies with Lemon Sugar from the oven and let them cool on the baking sheet for a few minutes. Then, transfer them to a wire rack to cool completely. Enjoy these delightful cookies with a cup of tea or coffee!