Slicing papaya: Cut into halves, peel, and discard seeds.With a sharp knife or --better-- a mandoline, slice the papaya very thinly.
Brining: Place the sliced papaya in a medium saucepan, add salt, and enough water to cover. Heat over medium heat until it breaks the boil. Immediately remove from the heat. Let it cool to room temperature.
Rinsing: Remove the papaya from the water, and discard the water. Add enough fresh water to cover it, stir to rinse out the salt, and discard the water.
Cooking: Place the papaya in a small pot or medium saucepan, add cinnamon sticks, cloves, and sugar. Add ⅓ cup of water.Simmer over medium-low heat until almost all the liquid (the papaya will release some as it cooks) evaporates.Discard cinnamon sticks and cloves.
Serving and storing: Cool to room temperature, then chill before serving.Store in a lidded jar and refrigerate for up to a week, or serve once chilled.
Pick a papaya that has green skin, and is very firm when pressed. Score the skin very shallowly to make sure no sap oozes out.Brown sugar gives this dessert a much darker color than if you use white sugar, this is a matter of preference.Slicing the papaya very thinly is also a matter of preference, you can also dice it, or slice it a bit thicker.