To make the dough, warm the vegan milk and sugar over medium-low heat until the mixture reaches a maximum of 110°F (45°C). Once the milk mixture is warm, remove from the heat. Sprinkle in the yeast and let it sit for 10 minutes until the yeast begins to foam.
Transfer the contents of the saucepan to a large mixing bowl (or the bowl of a stand mixer if you have one) along with the flour, nutmeg, vanilla, vegan butter and salt to the bowl. Mix until the dough starts to come together, then knead by hand or with a stand mixer using the dough hook attachment for 5-8 minutes until the dough is smooth and slightly elastic.
Cover the dough with a damp cloth and let it rise in a warm area for 1-1 ½ hours, until it has doubled in size.
For the filling, stir the vegan butter, sugar, and cinnamon in a small saucepan over medium heat until the sugar dissolves and the mixture is smooth.
Once the dough has risen, punch it down to release any air. Roll it out on a lightly floured surface into a rectangle about 20 by 12 inches (50 by 30 cm).
Spread the filling evenly over the dough, leaving a small border on the edges. Starting from the long side, roll the dough tightly into a log. Slice the log into 10 equal pieces.
Arrange the rolls in a lightly greased baking pan, cover with a damp cloth, and let them rise again in a warm location for 25-30 minutes until they puff up. *Alternately, you can place each bun onto a baking sheet lined with lightly greased parchment paper, leaving a couple inches of space between each bun. This is a way to form and bake them where the buns remain individual rather than becoming a pull-apart thing.
While the buns proof, preheat the oven to 350°F (175°C). Once risen, bake the rolls for 25–30 minutes, or until golden brown. If your oven has uneven heat, make sure to rotate the pan in the oven and perhaps switch it to another rack in your oven at the halfway point.
While the rolls bake, prepare the icing by whisking together the powdered sugar, plant-based milk, agave nectar or maple syrup, and vanilla powder or extract until smooth. If you are making the optional preglaze (I use it only if I am baking the rolls spaced out on a baking sheet), mix that up in a separate bowl.
If you are using the preglaze, use a basting brush to get the glaze into all of the little nooks and crannies. Allow the glaze to set before applying the icing.
Allow the rolls to cool slightly before drizzling the icing over the top. Serve warm.