One final note:  Fresh pumpkin is much, much better than canned. It’s very easy to prepare: cut open the pumpkin (or butternut squash), clean out the seeds, place cut-side down in a pan with a half inch of water, cover, and bake until soft (about an hour in a hot oven). When cool enough to handle, scoop out the flesh and mash with a fork until smooth. I let the pumpkin puree drain for about an hour in a fine-mesh strainer, as the excess water will cause problems with the texture of the pudding. 

Egg-free pumpkin pudding or pie filling

3/4 cup sugar
1/4 cup cornstarch
1/2 teaspoon salt
3/4 teaspoon ginger
3/4 teaspoon cinnamon
1/2 teaspoon nutmeg
scant 1/8 teaspoon cloves
 1  1/4 cups whole milk
3/4 cup cream
1 cup fresh pumpkin puree 

 In the top bowl of a double boiler, combine the sugar, cornstarch, salt, and spices and whisk to blend. Add about 1/8 cup of milk and whisk into a paste. Add more milk as needed, but be careful not too add too much milk at first, or the cornstarch will have lumps. Once you have a smooth paste, gradually add the rest of the milk and cream, then stir in the pumpkin. Place over simmering water on the double boiler and cook, stirring frequently. After about five minutes, stir constantly until the mixture thickens. Continue to cook for two minutes, then remove from the heat. Pour into ramekins to serve as a pudding or into a prebaked pie crust for a pie. Chill for at least a couple of hours, until firm.