Warm the plant-based milk and rum in a small saucepan over medium heat for 90 seconds, until the mixture is just warm to the touch but not hot. Remove from heat and stir in the sugar and yeast. Let stand for 10 minutes, until foamy.

In a large bowl, mix together the flour, fresh ginger, ground ginger, nutmeg, and salt.

Add the proofed yeast liquid to the dry ingredients along with the molasses, vanilla extract, and melted vegan butter. Stir until a shaggy dough forms.

Either knead in a stand mixer or transfer the dough to a lightly floured surface and knead for 8–10 minutes, until smooth and elastic. Place the dough in a greased bowl, cover, and let rise in a warm place for 1 hour, or until doubled in size.

While the dough rises, prepare the filling. In a small bowl, mix the softened vegan butter, brown sugar, ground ginger, and cinnamon until smooth.

Once the dough has risen, punch it down and transfer to a floured surface. Roll it into a 12 × 16 inch (30 × 40 cm) rectangle. Spread the filling evenly over the surface, leaving a 1-inch (2.5 cm) border on one long side.

Preheat the oven to 350°F (175°C). Bake for 25–28 minutes, or until golden brown and slightly firm to the touch.

While the rolls bake, make the icing by whisking together the powdered sugar, cream cheese, plant-based milk, cinnamon, nutmeg, ground ginger, molasses, and vanilla extract until smooth.

Drizzle the glaze over the warm rolls.

If desired, top with crushed gingersnap crumbs and place a gingerbread cookie on each roll while the glaze is still tacky before serving.