Mix dry ingredients: In a large mixing bowl or stand mixer bowl, whisk together the flour, sugar, baking powder, salt, ground nutmeg, and orange zest until well combined.
Add wet ingredients: Add the evaporated milk, softened margarine or butter, and eggs to the dry ingredients. Mix to form a dough.
Knead the dough: Knead the dough by hand or with a stand mixer until smooth. If sticky, sprinkle a clean surface with flour and knead until smooth, adding more flour as needed.
Roll and cut dough: Cut a small portion of dough and roll it out to about 1/8 inch thickness. Trim edges for uniformity if desired. Cut the dough into thin strips or squares using a sharp knife or pizza cutter.
Heat oil and fry: Heat neutral oil in a frying pan. Test the oil by dropping a piece of dough; if it floats quickly, the oil is ready. Fry chin chin in small batches, avoiding overcrowding, until golden brown.
Drain and cool: Remove fried chin chin with a slotted spoon and place on paper towels to absorb excess oil. Let cool completely.
Store: Store cooled chin chin in an airtight container at room temperature for up to one month.