In a skillet over medium heat, melt the butter, stirring occasionally as it foams and sizzles. After 5-7 minutes, it will turn golden brown with a nutty aroma, and the sizzling will slow down. Transfer to a small heat-proof bowl and let it cool for 2 hours or refrigerate for faster solidifying (about an hour).
Preheat the oven to 350°F. Line 2 cookie sheets with parchment paper.
Whisk together the flour, baking powder, baking soda, cinnamon, nutmeg, and salt in a medium mixing bowl. Set aside.
In a large mixing bowl, use an electric mixer to beat the brown butter, white sugar, and brown sugar until fluffy, about 3-4 minutes. Add the eggs one at a time, followed by vanilla, mixing until pale.
Gradually add the flour mixture to the wet ingredients until just combined. Try not to over-mix the dough. Fold in the oats, raisins, and pecans until evenly mixed.
Scoop 1-½ tablespoons of dough onto the parchment-lined cookie sheet, spacing each 2 inches apart. I can fit 12 cookies on a large (half-sheet) cookie sheet. You'll need to use the cookie sheets twice for 4 batches of cookies in total.
Bake each batch of brown butter oatmeal raisin cookies for 12 minutes or until the edges are golden and the centers are just set. Let the cookies cool for 10 minutes on the cookie sheet before transferring to a cooling rack.
Serve warm or at room temperature. Store the brown butter oatmeal raisin cookies in an airtight container.