Whisk the flour, salt, and baking soda together in a medium bowl. Set aside.
In a small saucepan over medium heat, melt 0.5 cup (1 stick) of the butter. Continue to cook, swirling occasionally, until the butter foams and brown specks form at the bottom of the pan, giving off a nutty aroma. Remove from heat immediately and transfer to a large heat-proof mixing bowl. Let cool for 1 minute.
Add the remaining 0.25 cup of butter to the warm browned butter and stir until completely melted.
Whisk the dark brown sugar and granulated sugar into the butter mixture until smooth.
Add the whole egg, egg yolks, and vanilla extract, whisking until fully incorporated and smooth.
Gradually fold the dry flour mixture into the wet ingredients using a rubber spatula until just combined. Fold in the chopped toasted pecans.
Cover the bowl and chill the cookie dough in the refrigerator for at least 30 minutes.
Preheat your oven to 350°F (175°C) and line two baking sheets with parchment paper.
Scoop the chilled dough into 1.5-inch balls and place them on the prepared baking sheets, spacing them about 2 inches apart.
Bake for 10 to 12 minutes, or until the edges are golden brown and the centers are just set. Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.
Notes
Store the cookies in an airtight container at room temperature for up to 5 days.