Pre-heat the oven to 350°F. Grease and flour a 9-inch springform pan and set aside.
Dice the butter and melt it in a saucepan over medium-high heat. Continue to cook the butter until it browns, about 8 minutes. Stir the butter as it browns to keep the butter fat from sticking and burning at the bottom of the pan. When done, the butter will be golden in color and very aromatic with a pleasant nutty smell. Remove the browned butter from the heat and strain through a mesh sieve into the bowl of a stand mixer (or large bowl with a hand mixer).
Meanwhile, whisk together the flour, baking powder, salt, cinnamon, ginger, and cardamom. Set aside.
Add the sugar to the browned butter and mix on medium speed for a couple minutes. Not only are we incorporating the sugar into the butter, but we are bringing down the temperature of the browned butter before adding the eggs. After mixing in the sugar, add the eggs and vanilla. Once the eggs are incorporated, add the sour cream and mix until combined.
Turn the mixer to low and add in the flour mixture in two batches. Stop the mixer before the dry ingredients are fully incorporated. Fold in the carrots and pecans, if using, until combined.
Tip about ⅔ of the batter into the prepared springform pan and smooth out with a small offset spatula or the back of a spoon. Sprinkle the top of the batter with the brown sugar and remaining cinnamon. Carefully spread the remaining batter over the top of the brown sugar mixture.
Sprinkle the Oat Streusel Topping over the top of the cake batter. Bake for 35 to 45 minutes, or until a toothpick inserted into the center of the cake comes out clean. Cool the cake on a wire rack before removing the the ring of the springform pan.
To serve, drizzle with the Vanilla Bean Glaze. Serve and store covered at room temperature for 3 to 4 days.