In a small bowl, whisk together 1 cups unsweetened plant milk (soy or oat, warmed to 110°F), the yeast (2.3 teaspoons active dry yeast), and 1 tablespoon of the sugar from 0.3 cups granulated sugar, divided. Let sit until foamy.

In a large bowl or stand mixer, combine the yeast mixture with remaining sugar, 4 tablespoons of the melted vegan butter from 6 tablespoons vegan butter, melted, divided, 3 tablespoons aquafaba (chickpea brine) or flax egg, 1 teaspoons salt, and 3.5 cups all-purpose flour, plus more for dusting. Mix until a soft dough forms.

Knead by hand or with a dough hook until smooth and elastic.

Place dough in a lightly oiled bowl, cover with a towel, and let rise in a warm spot until doubled in size.

Punch down the dough and roll it out on a floured surface into a large rectangle, about 16x12 inches.

Spread the softened vegan butter 2 tablespoons vegan butter, softened (for spreading) evenly over the dough. In a small bowl, mix 0.8 cups packed brown sugar (for filling) and 2 tablespoons ground cinnamon, then sprinkle evenly over the buttered dough.

Starting from the long edge, roll the dough tightly into a log. Slice into 12 even rolls using a sharp knife or unflavored dental floss.

Arrange rolls in a greased 9x13 inch baking dish, brush with the remaining 2 tablespoons melted butter from 6 tablespoons vegan butter, melted, divided, cover, and let rise again until puffy.

Preheat oven to 350°F (175°C). Bake the rolls until golden brown on top and cooked through.

Whisk together 1 cups powdered sugar (for glaze), 2 tablespoons unsweetened plant milk (for glaze), and 0.5 teaspoons vanilla extract until smooth and pourable.

Let rolls cool for 10 minutes, then drizzle generously with the glaze before serving warm.