Set the oven to preheat at a temperature of 350°F. Ensure a baking sheet is prepared with parchment paper.

Using a small pot, melt precisely 3/4 cup of the unsalted butter over medium heat. Consistently stir until the butter reaches a brownish hue. Once achieved, remove from the heat and integrate the remaining butter until it's fully melted.

Incorporate 1 1/2 cups of the brown sugar into the melted butter. Stir until the mixture attains a smooth consistency. Subsequently, add the egg, egg yolk, salt, and vanilla extract. Once all ingredients are fully integrated, set the mixture aside.

In a distinct bowl, combine 1/4 cup of granulated sugar, the remaining 1/2 cup of brown sugar, the all-purpose flour, and the baking soda. Ensure these dry ingredients are thoroughly mixed.

Gradually blend the butter and sugar mixture into the dry ingredient mixture until a consistent dough is formed.

Form the dough into spherical shapes and roll each in the residual 1/4 cup granulated sugar. Position them systematically on the prepared baking sheet.

Bake in the preheated oven for approximately 12-14 minutes, ensuring the cookies are slightly set. Although they may appear soft, they will gain firmness as they cool. Serve as deemed appropriate.