In a small saucepan, warm the soy milk and vegan butter over medium heat until the butter has melted. Do not boil it. Remove from the heat and stir in the mashed sweet potato.
In a large bowl, mix together the flour, granulated sugar, salt, and yeast. Pour the liquid ingredients into the dry and use a wooden spoon to combine. Once it gets too difficult to stir, use your hands to combine the ingredients.
Flour a clean work surface and transfer the dough onto the prepared work space. Knead it until you’ve got a smooth dough ball. Lightly oil a large bowl. Place the dough ball in it, cover with plastic wrap or a kitchen towel, and let rise for 1 hour. The dough should double in size.
Make the filling: In a small bowl, combine the brown sugar and cinnamon and set aside. Chop the pecans into small pieces and set aside. In a small saucepan, melt the vegan butter and set aside.
Once the dough has doubled in size, preheat the oven to 375°F (190°C).
Press the air out of the dough, then transfer it back onto your floured work space. Roll the dough until it is about ¼-inch (6 mm) thick. You should end up with a roughly rectangular oval, about 12x16 inches (30x40 cm).
Brush the dough with the melted butter, sprinkle with the cinnamon-sugar mix, and then top with the chopped pecans. Fold the short side of the dough over and roll tightly until you have a log.
Carefully cut the log into twelve 1-inch (2 cm) slices. Grease a large skillet or a 10-inch (25 cm) round baking dish and place the rolls in it cut-side down.
Bake for 25 minutes, or until they've expanded and turned slightly golden on top.
Meanwhile, make the frosting: Place all the ingredients in a food processor or standing mixer with the whisk attachment on high and blend until creamy.
Remove the rolls from the oven and let cool for 5 to 10 minutes. Top with the sweet potato frosting and serve immediately. They will stay fresh for up to 2 days, but they’re best eaten the day you bake them.