In a large mixing bowl or bread bowl, stir the brown sugar, and water in a large measuring cup until combined. Stir in yeast and allow to rest until frothy. If the yeast does not become active within 10 minutes, it is likely bad. Throw it out and begin again.
While the yeast is activating, in a Vitamix or Cuisinart, blend milk, salt, and avocado until creamy. Stir into bowl with yeast.
Gradually stir in wheat flour until incorporated, then stir in all-purpose flour with a dough whisk until you can no longer stir it. Set the whisk aside and begin kneading with your hands. Continue to knead for about four minutes and form into a soft ball, adding a little more flour if necessary. The ball should be slightly sticky but should not cling to your hands.
Cover with plastic, a clean towel or even a dinner plate and allow to rise for one to two hours or until doubled in size. Deflate ball of dough and weigh. Divide by ten. Each bun should weight somewhere between 138 and 149 grams.
Form balls and press into four-inch discs. Place each disc in the middle of a 4-inch greased springform pan. Place 10 of these pans in a half-sheet baking pan. Brush tops with eggless wash, cover with a clean cloth and allow to double in size. While they are rising, preheat oven to 355º.
Brush again with eggless wash and sprinkle with oats and sesame seeds. Bake in preheated oven on the middle shelf for seven minutes. If doubling the recipe, use the top and middle shelves. Turn the trays around and, if doubling the recipe, switch oven shelves. Cook for another seven minutes.
Allow to cool for five minutes in springform pans. Resist the temptation to eat these while they are hot. Release and carefully remove buns. (Alright, you can have one!) Transfer to a cooling rack and allow to cool thoroughly. Bread continue to cook as they cool so this is an important step. Allow to cool thoroughly before cutting. Enjoy!