Preparing the Dough:

1. In a large bowl, dissolve the yeast in warm water. Add the sugar and let sit for 5-10 minutes until frothy.
2. Add the vegetable oil, flour, and salt to the yeast mixture. Mix until a dough forms.
3. Knead the dough on a lightly floured surface for about 5 minutes, until smooth and elastic.
4. Place the dough in a greased bowl, cover with a damp cloth, and let rise in a warm place for about 1 hour, or until doubled in size.

Making the Filling:

1. In a small bowl, mix together the brown sugar, cocoa powder, cinnamon, and coffee granules.
2. Roll out the dough on a floured surface into a rectangle about 1/4 inch thick.
3. Spread the softened vegan butter evenly over the dough, then sprinkle the sugar mixture on top.

Assembling the Rolls:

1. Starting from the long side, tightly roll up the dough into a log.
2. Cut the log into 12 equal pieces and place them in a greased baking dish.
3. Cover the dish with a damp cloth and let the rolls rise for another 30 minutes.

Baking:

1. Preheat your oven to 350°F (175°C).
2. Bake the rolls for 20-25 minutes, or until golden brown.

Icing:

1. In a small bowl, whisk together the powdered sugar, brewed coffee, and vanilla extract until smooth.
2. Drizzle the icing over the warm rolls before serving.