Grease an 8x11-inch baking pan generously with softened butter. (The larger the baking pan, the less tall and fluffy the buns will be.)
Transfer the proofed dough to a flour-dusted surface. Divide into 6 equal pieces. Knead each piece to remove air bubbles, then roll it into a ball.
Rub a rolling pin with flour. Take one ball and flatten it with your palm.
Roll into a 5- to 6-inch circle, aiming to keep the middle thicker than the perimeter. (The larger the wrapper, the thinner the bun, so if you prefer to have a more doughy bun, roll a smaller wrapper.)
Divide the filling evenly between the circles, placing the mound in the middle of the circle. Bring up all the sides and pinch to seal. Place the buns seam side down on the greased baking pan, evenly spaced out. Cover with a kitchen towel and let rest for 15 minutes while you heat the oven to 375°F.
Meanwhile, make the vegan egg wash by whisking the milk and maple syrup until combined.
Brush the proofed bun with vegan egg wash and sprinkle some sesame seeds on top.
Bake the buns for 25 to 35 minutes, until the top turns golden brown. To get a shinier look, if you’d like, you can brush the baked buns with a thin layer of melted butter.