Heat almond milk until warm to the touch but not hot. Pour into a large mixing bowl.
Stir sugar and instant yeast into the warm milk. Let sit 2–3 minutes while you prep the next ingredients.
Add melted vegan butter and stir. Add flour gradually, mixing until a soft dough forms.
Turn dough onto a lightly floured surface and knead 5–7 minutes until smooth and elastic. Dough should feel soft, not stiff.
Place dough in a lightly greased bowl, cover, and let rise for about 1 hour or until doubled.
Roll dough into a rectangle about ¼-inch thick on a lightly floured surface.
Spread softened vegan butter over the dough. Mix brown sugar and cinnamon, then sprinkle evenly across the surface. Press lightly so it sticks.
Use a knife or pizza cutter to slice the dough into long strips, about 1–1½ inches wide. Roll each strip into a spiral and place on a parchment-lined baking sheet.
Take the loose tail end of each strip and loop it upward into two ears. Press the end gently into the top of the roll to secure.
Place the tray on the stove while the oven preheats. Let rolls rest and puff up for about 15 minutes.
Bake at 350°F for about 16 minutes until lightly golden.
half way through - around the 8-minute mark, remove the pan briefly and gently push the ears back together if they’ve spread. Return to oven to finish baking.
Brush hot rolls with melted vegan butter immediately after baking.
Beat vegan cream cheese until smooth. Add powdered sugar, almond milk, and vanilla. Mix until thick and creamy.
Spread icing over warm rolls and serve.