Warm dairy-free milk to 110°F, stir in 1 tbsp sugar and 1 tbsp flour, sprinkle in yeast. Cover and let activate 10 minutes.
Mix yeast mixture with remaining sugar, applesauce, melted vegan butter, and vanilla. Add flour gradually to form dough.
Knead lightly 2–4 minutes until smooth. Place in greased bowl, cover, and proof 1 hour.
Mix cinnamon and sugar for filling. Roll dough into rectangle, spread with butter, sprinkle filling evenly, and roll tightly. Slice into 12 rolls.
Place rolls in greased baking dish. Cover and proof 30 minutes while oven preheats to 375°F.
Pour vegan heavy cream between rolls before baking. Bake 20–22 minutes until golden.
Mix icing ingredients until smooth. Spread over warm rolls and serve immediately.
