Place almond milk, melted vegan butter, flour, sugar, salt, and yeast in the bread machine pan in the order recommended by the manufacturer. Select the Dough cycle and start.
Once the dough cycle is complete, turn the dough out onto a lightly floured surface and roll it into a rectangle.
Spread softened vegan butter over the dough. Mix brown sugar and cinnamon together and sprinkle over the buttered dough.
Roll the dough up tightly and cut into 12 rolls. Place the rolls in a greased baking dish. Cover and let rise for about 30 minutes.
Preheat oven to 375°F (190°C). Bake the rolls for 20-25 minutes or until golden brown.