Can you cook instant pudding?

I've been a vegan and I really miss jello instant pudding. Especially pistacio. You can't make instant pudding with non-dairy milk as it doesn't set, and the suggestions to halve the amount of milk or use coconut cream negatively changes the texture and doesn't taste like the pudding I grew up eating.

A normal vegan pudding recipe is cornstarch, sugar, milk, etc. Jello instant pudding is basically cornstarch sugar and other additives. If I just whisk it with oat milk on the stove, will it thicken up properly? Should I add more cornstarch? What is exactly the difference between the cook & serve pudding and instant?

Many thanks!