Using a mixer (or by hand), mix the dry ingredients: flour, baking powder, salt, sugar, nutmeg, and lime zest.
Mix the butter into the flour mixture until well incorporated.
Add the milk and egg to the mixture. Keep mixing until you form a sticky dough ball.
Dump the dough ball onto a floured surface and knead, incorporating more flour into the dough as needed, until the dough is smooth, elastic, and even in color and no longer sticky. You can create many shapes and sizes for chin chin.
Divide the dough in half. On a floured board, roll each half out until it's about ⅙ inch thick, just like linguine or fettuccine. A pasta machine works great if you have one. Then, cut the dough into any shape you desire.
Heat a deep cast-iron skillet, saucepan, or (my all-time favorite) a Dutch oven over medium heat. Add around 3 inches of oil and heat it to 375℉ (190℃). Fry chin chin in the hot oil until golden.
Remove them from the oil, drain, and serve.