Add the butter to a saucepan and melt it over medium heat. Continue cooking until the butter turns golden brown and develops a nutty aroma. Remove from heat and let it cool slightly.

Transfer the browned butter to a mixing bowl and let it cool for 5–10 minutes. Add the brown sugar and mix until well combined.

In a small bowl, combine the softened cream cheese, and vanilla extract until smooth.

Add the cream cheese mixture to the browned butter mixture and whisk until smooth and fully incorporated.

Add the flour, baking soda, and salt to the mixture.

Mix gently until a soft cookie dough forms.

Stir in the lemon zest and lemon juice until evenly distributed throughout the dough.

In a small bowl, combine the granulated sugar and lemon zest to prepare the lemon sugar coating.

Scoop portions of dough and roll them into balls. Coat each dough ball evenly in the lemon sugar mixture.

Place the coated cookie dough balls on a baking sheet lined with parchment paper, leaving space between each cookie.

Bake at 350°F (175°C) for 10 to 12 minutes, or until the edges are lightly golden.

Allow the cookies to cool completely on a wire rack.

In a small bowl, whisk together the powdered sugar, lemon juice, and lemon zest until smooth to make the glaze.

Drizzle the lemon glaze over the cooled cookies and allow it to set before serving.