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 risen, turn dough out onto floured countertop and press flat. Roll dough into a rectangle that's approximately 16 by 20 inches.

Spread softened butter over the dough, getting right to the edges, but leave a one inch band along the long edge at the top of the rectangle (furthest away from you).

Mix cinnamon and brown sugar in a small bowl, and then sprinkle evenly over the butter.

Wet your finger and run it along the 1 inch band of dough at the top that has no butter (this will help seal the rolls).

Begin rolling the dough up, starting with the long edge closest to you. Roll it up completely, rolling towards the bare edge that you pre-moistened.

Pinch your log of dough along the seam to seal it, and turn the ends under so the sugar mixture is completely enclosed within the log.

Slice the log into 12 pieces by cutting it in half, then each piece in half (so you have four sections). Cut each section into three evenly sized rolls.

Butter an 11 x 17' cookie sheet and/or line with parchment paper. Place the rolls on the pan in four rows of three, evenly spaced (place the ends cut side up).

Melt an additional 2 - 3 tablespoons of non-dairy butter and brush the sides of the rolls where they will eventually touch once risen (to make it easier to pull them apart). Brush any extra over the tops of the rolls. Cover with a piece of wax paper and a tea towel (or use plastic wrap) 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 covering, and bake rolls until golden, about 20 - 25 minutes.

Remove rolls from the oven, and allow to cool most of the way.

While rolls are cooling, combine cream cheese and butter in a medium sized bowl. Beat until well combined. Add remaining ingredients and beat until frosting is smooth.

When rolls are cool, but still slightly warm, spread frosting evenly over the top.

These are best eaten fresh, but can be made ahead of time and frozen, then thawed overnight and warmed in a low oven just before eating (be careful not to heat them too much or the frosting will melt and run off). Twenty or thirty seconds in the microwave also works well.