Add all the ingredients to a saucepan while everything is still cold. Whisk thoroughly until the cornstarch is completely dissolved and the mixture looks smooth with no lumps. Starting cold is important because it helps the pudding thicken evenly as it heats.

Place the saucepan over medium heat and continue whisking constantly. Use steady, gentle strokes and make sure to scrape the bottom and sides of the pan so nothing sticks or scorches. As the mixture warms, it will slowly become more opaque and creamy.

Keep cooking and whisking for several minutes until the pudding noticeably thickens and coats the back of a spoon. You should be able to draw a line through it with your finger and have it hold its shape briefly before slowly filling back in.

Remove the saucepan from the heat as soon as the pudding reaches a thick, smooth consistency. Immediately whisk in the coconut extract and vanilla extract, making sure they are evenly distributed throughout the pudding.

Pour the pudding into serving dishes or storage containers and let it cool slightly at room temperature. Cover and refrigerate for at least 2 hours, or until fully set and chilled. Serve cold, enjoying the creamy, silky texture and gentle coconut flavor.