In a small saucepan, heat plant-based milk and vegan butter until melted. Let cool to lukewarm.
In a large bowl, combine 3 ½ cups of flour, yeast, granulated sugar, and salt. Add the milk mixture and Just Egg, mix until combined. Gradually add the remaining flour until a soft dough forms.
Knead the dough on a floured surface for about 5-7 minutes, until smooth and elastic. Place in a greased bowl, cover, and let rise in a warm place until doubled in size, about 1 hour.
Roll out the dough into a 15x9 inch rectangle. Spread with softened vegan butter. Mix brown sugar and cinnamon, and sprinkle over the buttered dough.
Roll up the dough tightly and cut into 9-10 slices. Place in a greased 9x13 inch baking dish, round cake pan, or any dish you see fit! Cover and let rise until doubled, about 30 minutes.
Preheat your oven to 350°F (175°C). Bake the cinnamon rolls for 25-30 minutes, until golden brown.
While the rolls are baking, mix powdered sugar, plant-based milk, and vanilla extract to make the glaze. Drizzle over warm cinnamon rolls.