1 1/2 cups water
1 cup packed brown sugar
1 large Mexican cinnamon stick or 3 regular cinnamon sticks
1/2 pound pumpkin or acorn squash, peeled and cut into 2-inch cubes
1/4 cup heavy cream
1 1/2 pints to 2 pints vanilla ice cream
Combine the water, brown sugar, and cinnamon in a medium sauce pan. Bring to a boil and cook until the liquid has reduced by about one-quarter and a light syrup forms, about 15 minutes. Add the pumpkin or squash, reduce the heat to very low and simmer gently until the pumpkin is translucent, about 45 minutes.
If preparing in advance, remove the pumpkin from the syrup with a slotted spoon and store the pumpkin and syrup separately. When ready to serve, combine the pumpkin and syrup in a small skillet and reheat over low heat.
Just before serving, stir the heavy cream into the pumpkin syrup. Spoon over the ice cream and serve.