Heat milk and water until just warm/body temperature. Pour into bowl of stand mixer (or large bowl). Add sugar, stir to combine, then sprinkle over with yeast. 

Measure and melt butter; measure flour. Gather remaining ingredients.

Ensure yeast is alive and active (it should look foamy after several minutes; if not, you might have to replace it with fresh yeast). If the yeast looks good, add salt, aquafaba, melted butter, and flour to the bowl with the liquids. Stir (use the dough hook if using a mixer, the handle of a wooden spoon if doing it by hand) until well combined (a minute or so). Dough will be somewhat sticky.

Leave dough in bowl; cover with a plate or something to keep dough from drying out. Let rise in a warm place until doubled in size (about an hour and a half).

Once dough has risen, prepare large baking pan or sheet by coating well with non-dairy butter (you can make 12 large buns in a 9 x 13 pan, or 24 smaller rolls in a 13 x 18 half sheet pan). On a floured surface, punch down dough and divide into the appropriate number of pieces (I cut the ball into four equal pieces, then each of those into two, and each of those into three, to get 24 rolls). Form each piece into a tight ball by tucking the sides down and under until you have a smooth, seamless top.

Melt an additional 2 - 3 tablespoons of non-dairy butter and brush half of it across tops and sides of the rolls. Cover with a damp tea towel and set aside to rise until doubled (about 30 minutes). 

About 15 minutes before baking, preheat oven to 375 degrees F.  

Once rolls have risen, remove towel, and bake rolls until golden, about 20 - 25 minutes.

Remove rolls from the oven, and immediately brush tops with another thin coating of butter. Slide onto cooling rack, and let cool slightly before serving.