Preheat the oven to 350 °F (175 °C). Grease two 6-muffin pans and set aside.
Put the butter in a small saucepan and heat on high to brown the butter. Transfer to a bowl and let cool.
In a large bowl, whisk together the eggs, vanilla extract, buttermilk, sugar, and maple syrup. When the wet ingredients are really well mixed, add in the All-Bran and stir. Set aside.
In a separate medium bowl, whisk the flour, baking soda, and salt.
Remove one tablespoon of the flour mixture and add it to a small bowl with the chopped dates. Toss them to coat them in flour and break apart any clumps of dates.
Add the rest of the dry ingredients to the bowl with the wet mixture. Mix everything together to form a thick batter. It's okay if you still see a little flour at this stage.
Stir in the browned butter and then the floured dates, and stir until the batter is just mixed (don't overwork it!).
Divide the muffin batter between the two pans. You may garnish the tops with a few extra pieces of chopped pitted dates if you have extra dates.
Bake for about 22 minutes or until they have puffed and the edges are beginning to brown.
Let cool in the pan for 5 or so minutes before twisting each of the muffins to release them onto a wire rack to cool. Serve warm with lots of butter and salt.