Stir together the milk, sugar, water, and butter in a microwave-safe dish. Heat for 30 seconds in the microwave. Set aside to cool slightly. The temperature should be approximately 105°F (if you don't have a thermometer, you should be able to stick your finger into the mixture and not feel a noticeable difference). Sprinkle the yeast over the top and stir together. Set aside.
Sift together the flour, salt, and vital wheat gluten in a large bowl.
Stand Mixer Instructions: Pour the flour mixture into a mixing bowl of a stand mixer. Pour in the yeast mixture. Add the dough hook attachment to the mixer and mix on low speed, stopping occaisionally to wipe down the sides of the bowl and the dough hook. Continue on low speed (kneading the dough) for 5 minutes.
Remove the dough from the bowl and place on a lightly floured surface. Knead into a ball. You should be able to press a finger in the dough and the impression you left fills back quickly. That will let you know the dough is ready.
By Hand Instructions: Pour the yeast mixture in with the flour mixture and using a rubber spatula, stir to combine. Once the dough has formed into a ball, transfer to a floured surface and continue kneading for 5 minutes. You should be able to press a finger in the dough and the impression you left fills back quickly. That will let you know the dough is ready.
Rinse out the bowl you used for mixing the dough and either spray with vegetable spray or coat with a thin layer of olive oil. Place the dough in the bowl, cover with a wet dish towel or plastic wrap. Set aside in a warm place until the dough has doubled, about an hour.
Preparing Buns: When the dough is ready, line two baking sheets with parchment paper or spray the pan with vegetable spray.
Cut the dough in half. Then shape each half into rectangles. Cut each half into four equal pieces, to make 8 total pieces. Roll each piece into balls. Then roll the ball between your hands or between the palm of your hand and the counter, to roll it out into a cylindar that measures between 5 - 6" long. Place on prepared pan. Continue with remaining dough, place rolled dough about 1" apart on the pan.
Spray one side of a sheet of plastic wrap with vegetable cooking spray. Place oiled side down over the rolls. Set aside to rise approximatley 30 - 40 minutes.
Baking Buns: When you're ready to bake the buns, place one rack on the top level and one in the middle of the oven. Preheat oven to 375°F.
Prepare the vegan egg wash by combining the milk, butter, and syrup in a small bowl. Gently brush the top of each bun with vegan egg wash and sprinkle with sesame seeds.
Place the pan in the center rack and bake the buns for 15 minutes. Use an oven mitt to move the pan to the top rack and turn on the broiler. Broil for 1 - 3 minutes, until a nice golden brown crust is achieved. Remove pan from oven and use tongs to place buns on a wire rack to cool
Allow buns to cool for 5 minutes then they're ready to serve. Slice buns and toast before adding your desired fillings. To store, allow buns to cool, then place in an airtight container. They are best when fresh, but they can keep 1 - 3 days at room temperature, or up to 5 days in the fridge. These buns can be frozen for up to 2 months.