Combine the warm water and the sugar in a small bowl. Sprinkle the active dry yeast over the top and set aside for 5 minutes.
In the meantime, add the plant milk, melted vegan butter, and sugar to a large bowl and mix until well combined. I like to use my Kitchenaid, but a bowl works just fine.
Add the mixture of water, sugar, and yeast to the bowl, and mix again.
Combine the salt and the flour in a separate bowl and add half of the flour mixture to the dough. Stir until well combined. Then add the remaining flour and stir again.
Knead for 3 to 5 minutes until smooth, sprinkle with more flour if needed, and form into a ball. I like to knead my dough for 5 minutes in the Kitchenaid mixer, but you can also use your hands. It’s okay if the dough is slightly sticky, but if it’s too sticky, you can add a little more flour.
Grease a large bowl with some oil and transfer the dough into it. Cover with a dishcloth and let it rise for 1 hour in a warm place or until it doubles in size.
Place the dough onto a well-floured surface. Roll it out into a large rectangle, about ½-inch (1 cm) thick using your hands or a rolling pin. Sprinkle more flour on top while rolling to prevent sticking.
Spread the softened vegan butter evenly over the dough.
Sprinkle the brown sugar and then the cinnamon on top of the vegan butter.
Roll the dough lengthways into a tube shape. Roll it as tightly as you can. Place it seam side down. Cut off the two ends (this is optional but will make your cinnamon rolls look better). Then slice it into 12 rolls.
Grease a 9×13 inch baking dish (about 23×33 cm) with some oil or vegan butter.
Transfer the rolls to the baking dish, cover with a dishcloth, and let it rise for 30 minutes in a warm place.
Now it’s time to prepare the frosting! In a medium-size mixing bowl, whisk together the powdered sugar, plant milk, and vanilla extract until smooth.
Preheat the oven to 350ºF or 180ºC.
Bake the cinnamon rolls for 25 to 30 minutes or until golden brown.
Allow the cinnamon rolls to cool for about 10 minutes before drizzling with the icing.