In a large bowl, combine warm almond milk, sugar, and yeast; let sit for 5-10 minutes until foamy.
Stir in melted vegan butter, salt, and 2.5 cups of flour until a dough forms.
Knead the dough on a floured surface for 5-7 minutes, adding remaining flour as needed, until smooth and elastic.
Place dough in a greased bowl, cover, and let rise in a warm place for 1 hour or until doubled in size.
Punch down dough and roll out on a floured surface into a 12x18 inch rectangle.
Spread softened vegan butter over dough, then sprinkle evenly with brown sugar and cinnamon.
Roll the dough tightly from the long side and cut into 12 even rolls using a serrated knife or dental floss.
Place rolls in a greased 9x13 inch baking pan, cover, and let rise for 30-45 minutes.
Preheat oven to 350°F (175°C) and bake rolls for 20-25 minutes until lightly golden.
Whisk powdered sugar, 2 tbsp almond milk, and vanilla until smooth; drizzle over warm rolls before serving.