In a mixing bowl, combine the all-purpose flour, granulated sugar, baking powder, salt, and ground nutmeg. Mix well.
Add the softened vegan margarine or coconut oil to the dry ingredients. Using your fingers or a pastry cutter, rub the margarine or oil into the flour until the mixture resembles coarse crumbs.
Gradually add the plant-based milk to the flour mixture, a little at a time, and mix until a firm dough forms.
Transfer the dough to a clean, floured surface. Knead the dough for a few minutes until it becomes smooth and elastic.
Roll out the dough to about 1/4 inch thickness using a rolling pin.
Cut the rolled dough into desired shapes, such as squares or rectangles, using a knife or cookie cutter.
Heat vegetable oil in a frying pan over medium heat. The oil should be about 2 inches deep.
Gently place the cut-out chin chin into the hot oil, being careful not to overcrowd the pan. Fry the chin chin until they turn golden brown and crispy, about 3-4 minutes per side.
Use a slotted spoon to transfer the fried chin chin to a plate lined with paper towels. This will help absorb any excess oil.
Repeat the frying process with the remaining dough.
Allow the fried chin chin to cool completely before serving or storing in an airtight container.