Melt the vegan butter in a small saucepan on the stovetop. It shouldn’t boil.
Place the brown sugar, the almond milk, and the melted vegan butter in a large bowl. Stir with a wooden spoon until combined. Let it cool slightly for about 2 minutes. It should be warm but not hot.
Sprinkle the yeast over the mixture. Let it sit for 5 minutes. The yeast should be foamy.
Then add the flour, the cinnamon, and the salt and stir with a wooden spoon until combined. The dough will be sticky.
Cover the bowl with a towel and set in a warm place for 1 hour. It will rise and should about double in size.
Place on a floured surface. Knead with your hands. Then use a rolling pin and roll it out into a rectangle (about 24x15 inches, but you don’t have to be exact). The dough should be about ¼ inch thick.
Melt the vegan butter and spread the melted butter evenly over the dough rectangle. Sprinkle with sugar and cinnamon.
Starting at one of the short ends, tightly roll up the dough and seal the edges. Place it with the seam side down.
With a sharp knife, cut the roll into 12 equal pieces.
Generously grease an 8x8-inch square pan (or round pan) with vegan butter. Place the cinnamon rolls in the pan with the cut-side up.
Cover with plastic wrap and let rise in a warm place for about 45 minutes.
Preheat the oven to 350 °F. Remove the plastic wrap and bake for 25- 30 minutes until lightly golden.
In the meantime, make the vegan cream cheese frosting. Place all of the ingredients in a mixing bowl and mix with an electric mixer until well-combined and fluffy.
Let the cinnamon rolls cool down for about 10-15 minutes. Then evenly spread the cream cheese icing on top.