Peel and shred the apple and set aside. In a medium saucepan over medium heat, add the 1/2 cup of water and 3/4 cup of sugar. Stir to incorporate the sugar into the water. Add the 12 ounces of cranberries and continue stirring.
Add the shredded apple, 1 teaspoon of cinnamon, 1/2 teaspoon cloves, 1/2 teaspoon of vanilla, and a squeeze of lime juice. Stir to combine everything. It won't take long before the mixture starts to boil and the cranberries start to pop.
In a small measuring cup, mix the 2 tablespoons of cornstarch and 2 tablespoons of water until they are completely combined. Slowly stir the cornstarch slurry into the cranberry sauce.
Let the sauce boil a 2 more minutes as you stir intermittently, preventing the sauce from burning. The sauce will start to thicken as it boils.
After 2 minutes, remove the pot from the heat, add the 1 tablespoon of lime zest, and continue to stir for 1 more minute before putting in a glass dish to further cool down. The sauce will continue to thicken as it cools. I let the sauce sit out until the dish is just a bit warm to the touch, then I cover it and set it in the fridge.