Warm the soy milk to about 110 F (43 C) in a small saucepan or microwave-safe cup until it feels like bathwater. Stir in the melted vegan butter, granulated sugar, and instant yeast, then let it sit for 5 minutes until the surface turns foamy. If nothing bubbles, the milk was too hot and killed the yeast, so start again before adding flour.

Add the salt and the flour to the yeast mixture. Stir until a shaggy dough forms, then turn it out onto a lightly floured surface and knead for 8 to 10 minutes, until the dough is smooth, soft, and springy when you press it with a finger. Add flour a tablespoon at a time only if the dough is truly sticking.

Place the dough in a lightly oiled bowl, cover with a clean towel or plastic wrap, and let it rise in a warm spot until doubled in size, 1 to 1 1/2 hours.

On a lightly floured surface, roll the dough into a large rectangle, about 18 by 12 inches. Spread the softened vegan butter evenly across it, leaving a thin border on the far edge so it can seal. Mix the brown sugar and cinnamon together in a small bowl and sprinkle evenly over the butter.

Starting at a long edge, roll the dough up tightly, pressing gently as you go. Pinch the seam shut. Cut the log into 12 even pieces using unflavored dental floss or a very sharp serrated knife, wiping the blade clean between cuts.

Arrange the rolls cut-side up in a greased 9 by 13-inch baking dish, leaving a little space between them. Cover with a towel and let them rise again until puffy and touching, 30 to 45 minutes.

Heat the oven to 350 F (180 C). Bake the rolls for 22 to 25 minutes, until the tops are golden and the centers are set but still soft. Don't let them go dark brown on top or they'll turn dry. Let them cool in the pan for about 10 minutes.

Meanwhile, beat the softened vegan cream cheese and vegan butter until smooth, then add the powdered sugar, vanilla, and the tablespoon of soy milk, beating until glossy. Spread the frosting over the warm rolls and serve.