In a mixing bowl, combine the all-purpose flour, sugar, baking powder, salt, and nutmeg (if using). Mix well.
Make a well in the center of the dry ingredients and add the plant-based milk, water, and vanilla extract.
Mix the wet and dry ingredients together until a sticky dough forms. If the dough is too dry, add a little more water, one tablespoon at a time, until the dough comes together.
Knead the dough for about 5 minutes until it becomes smooth and elastic.
Cover the dough with a clean kitchen towel and let it rest for about 10 minutes.
Heat vegetable oil in a frying pan or deep pot over medium heat. The oil should be about 2-3 inches deep.
Pinch off small portions of the dough and shape them into round balls using your hands.
Gently drop the buns into the hot oil, being careful not to overcrowd the pan. Fry the buns until they turn golden brown, about 3-5 minutes per side.
Use a slotted spoon to transfer the fried buns to a plate lined with paper towels. This will help absorb any excess oil.
Repeat the frying process with the remaining dough.
Serve the Nigerian Buns warm as a snack or dessert.