Add a splash of cold water to 4 ramekins or small jars and swirl it around (making them wet will help the tembleque release once inverted). This is how it’s typically served, but if you want to make it easy on yourself and eat it straight out of the ramekin or jar, then don’t bother!
In a medium pot, add the coconut milk, sugar, lime zest (if using), ginger (if using), salt, and vanilla. If your coconut milk is lumpy, turn the heat on just for a little bit and whisk until it’s smooth. Turn off the heat and whisk in the cornstarch, sprinkling a little bit at a time and whisking thoroughly each time you add more. Once it’s all mixed in, whisk vigorously for a minute or so to really make sure there aren’t any clumps.
Place the pot over medium-low heat, stir in the lime juice (if using), and use a wood spoon or rubber spatula to constantly stir the mixture for about 7-10 minutes or until it thickens up to the consistency of a thick aioli/mayonnaise. Make sure you are scraping the edges of the pot to make sure nothing is getting stuck down there. After 5 minutes, you should start to see it thicken up. If it starts bubbling, turn your heat down. You want to cook it over a gentle heat slowly.
Divide the mixture between the prepared ramekins or jars. Let sit for 10 minutes on the counter to cool, then cover them and transfer to the fridge to set for at least 4 hours or overnight.
To release them from the jars, rub a knife along the sides and then invert it onto a plate. Shake and tap until you see/hear it release. If it’s not releasing easily or didn’t set enough, just eat it out of the jar.
Serve topped with desired toppings!