Prepare the squash. Peel the ayote and remove the seeds. Cut it into medium sized chunks, approximately 2 inches wide. Ensure the pieces are evenly sized to cook uniformly.
In a large pot, combine the water, brown sugar, cinnamon sticks, cloves, vanilla extract, and a pinch of salt. Add the orange peel if using. Stir to dissolve the sugar, then bring the mixture to a boil over medium heat.
Once the syrup starts boiling, reduce the heat to low. Let it simmer gently for 5–10 minutes to allow the spices to infuse their flavours into the syrup.
Carefully add the squash chunks to the simmering syrup. Arrange them in a single layer to ensure even cooking. If necessary, gently stir to coat each piece with the syrup.
Cover the pot and let the squash cook over low heat for 20–25 minutes, or until the pieces are tender but not falling apart. Test doneness by piercing a chunk with a fork, it should slide in easily but still hold its shape.
Uncover the pot and continue simmering for an additional 10 minutes, allowing the syrup to thicken slightly. During this time, occasionally spoon the syrup over the squash for a glossy finish.
Remove the pot from heat and let the squash cool slightly in the syrup. This step enhances flavour absorption and makes the dish easier to handle when serving.
To serve, arrange the squash chunks on a plate and drizzle generously with the thickened syrup. For an authentic presentation, serve warm with a dollop of cream or alongside soft bread to soak up the syrup.