Gather refrigerated ingredients on the counter to bring to room temperature.
Heat oven to 350 degrees F. Mix together the cake mix and oil. Press on the bottom of a 9" springform pan. Bake for about 10 minutes or until set. (if making cupcakes, bake for only a couple minutes and press into liners lightly). Set aside.
Turn down oven to 275 degrees F. Place a pan half filled with water on the lowest rack.
Beat cream cheese until fluffy on lowest speed. Gradually incorporate sugar, extract, and food coloring. One at a time, add the eggs, beating after each addition. Beat in flour until incorporated and stir in chocolate chips.
Pour batter into cheesecake pan. Drop the pan on the table repeatedly to release air bubbles and draw a sharp knife around in the batter to draw up air bubbles.
Bake for about an hour (if cupcake-sized, check after about 30 minutes). Do NOT open the oven door until the end of baking. To check if done, carefully move the pan. If the sides look firm and the center wobbles, the cheesecake is done. Turn off the oven heat and leave the cheesecake in the oven to cool with the door propped open. After an hour or so, let the cheesecake cool on the counter. When the sides of the pan are cool, put the cheesecake in the refrigerator. Do NOT cover the cheesecake (condensation will gather and drop water on top). A full-size cheesecake will be chilled enough to eat the next day, cupcakes can be eaten the same day once chilled.
To decorate, melt the chocolate and mix with the corn syrup. Place inside a plastic bag, and cut a tiny hole into the corner of the bag. Pipe onto the cheesecake.
To cut, run a sharp knife under hot water and wipe dry. Do this each time you cut a slice to get clean slices.