I prefer using JUST Egg as my egg replacer, but if using a flax seed mixture: Combine the flax seeds and warm water in a small bowl. Stir to combine. Set aside.
Add the yeast, milk and sugar to the large mixing bowl. Stir well to dissolve the yeast. Cover with parchment, plastic wrap or a towel and set aside for five minutes.
Uncover the yeasted mixture and add in the softened butter, ½ cup of the egg replacer of choice (JUST, flax...), salt and one cup of the flour. Mix by hand or with a mixer. Add in the second cup, repeat mixing. Then the third cup. Repeat mixing and finally, the forth cup of flour. By now, your dough should be nice and sturdy - enough to be able to knead either in the bowl or on a floured flat surface - like a counter. Knead for a few minutes until as smooth and fluffy as possible.
Spray your large mixing bowl with a bit of oil (optional) and place the dough into the center. Cover with plastic wrap, parchment or a clean dish towel. If using parchment, place something heavy on top to seal the edges. Set aside to rise for at least one hour, but usually 90 minutes for my dough. It will not double in size, but it will increase in size. This is fine.
When your dough is ready, pull it out and place it on a well-floured flat surface like a countertop. Roll the dough out to about a ten by fifteen shape. It does not need to be perfect! You want it to be about ¼ - ½ inches thick.
Pour or brush the melted butter all over the top side of the dough. evenly distribute all the filling ingredients - paying attention to even the edges. Sprinkle the cinnamon and sugar over top as well.
Roll the dough into a tight spiral and use a knife to portion out 9 equal pieces.
Line your casserole dish with parchment paper. Add the rolls to the dish. Cover again for a second rise. I usually do 30-60 minutes. You want the dough to expand even more.
Preheat oven to 350 degrees.
When dough is ready, place dish in the oven and bake for 25-30 minutes at 350 degrees. The edges should be lightly browned and tops poofy.
While baking, mix your frosting together in a medium bowl. You want it smooth and fluffy. Place in fridge until needed.
Pull rolls from the oven and allow them to cool for at least ten minutes until frosting. If you want your frosting to stay super thick, allow your rolls to cool for longer - a half hour should do it.
Serve warm! Store leftovers in the fridge.