Preheat oven to 375º F. Grease or paper-line 18 standard-sized muffin cups.
Combine flours, baking powder, baking soda, cardamom, and salt in a large bowl. Whisk until well mixed.
In a separate bowl, mix mashed banana, sugar, eggs, buttermilk, and butter until well combined.
Add the wet ingredients to the dry and mix until just combined. Fold in the crystallized ginger and about 3/4 of the chocolate chips.
Divide the batter equally between muffin cups with a spoon or ice cream scoop. Sprinkle remaining chocolate chips over the tops of the muffins.
Bake in preheated oven until the muffins are set and a toothpick inserted in the center comes out clean, about 20 minutes.
Let the muffins cool in pan for about 5 minutes before removing to a rack. Serve warm.