Start by activating the yeast. Add the water, brown sugar, and yeast to your mixing bowl. Mix them to incorporate, then let it sit for about 5 minutes.
Add the flour, salt, and oil. Start mixing on medium speed or knead by hand. Mix for 1 minute on medium speed and check the dough. It should feel just SLIGHTLY sticky or tacky.
If you need to add a tablespoon or 2 of water or flour. Turn the mixer on medium and mix for 7-8 minutes until the dough is smooth.
Cover and let it rise for 45 minutes to 1 hour. It should be just about doubled. Line 2 baking sheets with parchment paper.
Divide the dough into 8 equal pieces. Roll each piece into a ball and place 5 balls on each baking sheet, be sure to give them several inches between each other.
Spray the top of the balls and cover with plastic wrap. Place another sheet pan on top to lightly weight it down. Let it rise like this for 20 minutes. Remove the pan.
Preheat the oven to 400 degrees. Mix together the egg wash. When the oven is preheated, remove the plastic wrap, brush with the egg wash, then top with your toppings.
Move to the oven and bake for about 18 minutes, until the buns are golden brown. Remove them from the oven. Let them cool for at least 30 minutes before serving.