Wash the tejocotes and remove the stems. Bring a large saucepan of water to a boil. Add the whole fruit and blanch for 3–5 minutes, just until the skins loosen. Drain and cool until comfortable to handle.

Peel off loosened skins if desired. Halve the fruit carefully and remove all hard pits and any hard fragments with a small knife. Keep the fruit halves as intact as possible.

Put the piloncillo, 3 cups water, cinnamon stick and cloves into a wide saucepan. Bring to a gentle simmer, stirring until the sugar dissolves.

Add the prepared fruit halves. Simmer gently, partly covered, for about 20–35 minutes, turning carefully as needed, until a small knife slides easily through the flesh. Check early; ripeness and fruit size change the time.

If the fruit is tender while the syrup is too thin, lift the fruit into a bowl with a slotted spoon. Simmer the syrup uncovered for 5–10 minutes until lightly thickened but still pourable, then return the fruit. Avoid boiling it into a heavy glaze.

Remove from the heat and stir in the lime juice. Remove the cinnamon stick and cloves. Divide into 8 dessert portions with syrup and serve warm at a comfortable temperature or chilled. Refrigerate leftovers promptly; this is not a shelf-stable canning recipe.