To make the wet mixture, whisk together the brown butter, milk, sugar, vanilla, egg, and salt. Heat the mixture in the microwave for 30 to 60 seconds, or until it is warm to the touch but not hot. When yeast is added, this will aid in its activation.
Flour and quick yeast should be added. Knead the dough for about 12 minutes with a stand mixer that has a dough hook attached to it. Due to the enriched nature of the dough, it will take some time for the gluten to fully develop, and hand kneading will require twice as much time (oil your hands if you do to help with the stickiness). To the touch, the dough should feel tacky but not sticky.
Create a ball out of the dough and set it in a freshly oiled bowl. It should double in size after an hour of being covered and allowed to rise in a warm environment.
After the dough has risen, split it into four pieces and punch it down. Lay each piece out flat. Roll each one out again after folding it like a book. To get those fluffy layers, repeat this process twice. Make four rolls in total, then lay them in a buttered 9 x 5 loaf pan.
Cover your dough after shaping it to allow it to rise again for at least 30 minutes. Set the oven to 350 degrees Fahrenheit in the interim.
Bake the dough for 20 to 25 minutes after eggwashing it. This may change based on the oven you use. When your bread is finished, look for a top that has a good brown crust. Enjoy it while it's still warm and brush the top with melted honey for a sheen!