Preheat the oven to 350° F. Grease a 6-cup doughnut pan or 12-cup muffin pan with melted butter.

In a mixing bowl, stir together the melted butter, eggs, vanilla, maple syrup, brown sugar, and milk until combined.

Add the flour, baking powder, baking soda, cinnamon, cardamom, and salt, and mix until just combined.

Divide the batter evenly among the prepared pan, filling 1/2-2/3 of the way full. Bake for 12-13 minutes, until just set.

Remove and let cool for 5 minutes, then run a knife around the edges to release and invert the pan.

Meanwhile, make the glaze. Add the butter to a small pot set over medium heat. Allow the butter to brown slightly until it smells toasted, about 2-3 minutes.

Remove from the heat and whisk in the maple syrup, powdered sugar, and vanilla.

Dip or drizzle the doughnuts into the glaze.