Preheat oven to 350°F. Spray donut pan with non-stick spray and set aside.
Use a food processor to finely grind ¼ cup of toasted pecans.
In a small bowl, whisk together the flour, baking powder, baking soda, cinnamon, salt, and finely ground pecans.
In a separate bowl, whisk together the brown butter, brown sugar, and maple syrup until smooth. Add in the eggs and vanilla and whisk until fully incorporated.
Mix half of the dry ingredients into the egg mixture, then add in the milk. Once incorporated, add in the remaining dry ingredients and mix until just combined.
Transfer the batter to a piping bag, then cut off the tip and pipe into the donut pan, filling about halfway. You can also just spoon the batter into the pan if desired.
Bake at 350°F for 8-10 minutes or until a cake tester comes out clean. Invert the donut pan on a cooling rack, and the donuts should slide right out!
In a small bowl, whisk together the powdered sugar, maple syrup, melted brown butter, and salt. Slowly mix in milk a little at a time until your desired consistency is reached. The glaze should be thick but still pourable.
Dip the maple donuts into the glaze and place back on the cooling rack so the excess can drip off. Then sprinkle with chopped toasted pecans. The donuts are easy to glaze if they are cool, but they taste amazing when they're warm, so it's up to you!
These brown butter maple pecan donuts are best eaten the same day, but will keep in an airtight container at room temperature for up to 3 days.
Notes
To make brown butter, melt unsalted butter over medium heat, stirring frequently. Watch closely for the butter to develop brown specs and a nutty aroma. Once you start seeing brown specs, let cook for just a few seconds longer (watch very carefully or it will burn). Remove from the heat and pour into a small bowl so that it doesn't continue to cook. Set aside and let cool for at least 20 minutes. Note: For every ½ cup (1 stick or 113g), you'll lose about 1 tablespoon (14g) to evaporation while cooking. So you can either add in an extra 1 tablespoon before browning, or if you're browning big batches, just make up the weight difference in your recipe with regular unsalted butter if needed.