Brown the Butter: In a medium saucepan, melt the butter over medium heat. Continue cooking, swirling the pan occasionally, until the butter turns a deep golden brown and has a nutty aroma. This should take about 5-7 minutes. Be careful not to burn the butter. Once browned, remove from heat and allow to cool slightly.
Preheat your oven to 350°F (175°C) and line two large baking sheets with parchment paper or silicone mats
In a separate bowl, whisk together the flour, baking soda, and salt.
In a large mixing bowl, whisk together the browned butter, brown sugar, and granulated sugar until well combined.
Add in the egg and beat well, followed by the vanilla extract. Whisk until smooth.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Stir in the oats, and if desired, fold in the chopped pecans.
Using a large ice cream scoop, scoop the dough into 1.5-tablespoon-sized balls and place them on the prepared baking sheet about 2 inches apart. Bake for 10-12 minutes, or until the edges are golden and the centers remain soft. The cookies will firm up as they cool.
Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.