Cream the Brown Butter with both sugars in a stand mixer until well combined.
Beat the eggs in a separate bowl. Add the vanilla and stir to combine. Add to the butter/sugar mixture and mix well.
Combine the flour, salt and baking soda in a separate bowl. Mix carefully into the egg/butter mixture until well combined. Add the quick-cooking oats and mix well again. Add the finely chopped pecans and mix well to combine.
Divide the dough in half and place each half of the dough on a sheet of waxed paper. Roll the dough into a log and wrap it tightly in the waxed paper. Now you can either chill or freeze the dough until later, or you can go ahead and slice and bake the dough.
When you are ready to bake, preheat the oven to 350 degrees F.
Slice the dough 3/4-inch-thick, then place on a cookie sheet about 2 inches apart. Bake until they are golden brown, about 10 minutes. Let cool on the cookie sheets.
Add the butter to a medium skillet over medium heat. Allow it to melt and bubble up, swirling the pan to keep the butter moving around, for 3 to 4 minutes. When the butter is a medium golden brown, remove the pan from the heat (it will continue browning in the pan over the next 30 seconds or so!). Pour the butter (and any solids in the bottom of the pan) into a heatproof bowl and allow it to cool completely, about 30 minutes.