Step 1Combine the water and baking soda in a medium saucepan and bring to a boil. Add the papaya pieces and cook for 5 minutes over medium heat. With a slotted spoon, carefully transfer the fruit strips to a platter lined with paper towels; set aside.
Step 2Meanwhile, toast the cloves in a small skillet until fragrant, about 1 minute, and lightly crush them. Add the crushed cloves, piloncillo, granulated sugar and cinnamon to the papaya cooking liquid and cook over medium-high heat until the syrup is thick enough to thinly coat the back of a wooden spoon.
Step 3Return the papaya to the pan and cook for 30 minutes over medium heat. The syrup will turn a very dark amber. Let the papaya cool in the syrup, then transfer it, along with the syrup, to a bowl. Cover and refrigerate overnight.
Step 4The next day, put the heavy cream in a cold mixing bowl and whisk or beat, slowly adding the powdered sugar, until it holds soft peaks. Fold in the sour cream.
Step 5Drop 1 tablespoon of the queso blanco into each of 8 chilled martini glasses. Lay 4 slices of candied papaya on top. Add another tablespoon of crumbled queso blanco, then 4 more papaya slices. Drizzle some of the syrup over each, then spoon a dollop of whipped cream on top. Garnish each parfait with grated coconut, toasted for 13 to 15 minutes in a 350-degree oven, or mint leaves, as desired.