Preheat oven to 325° F.
To prepare the caramel sauce: Have a 9-inch round, dark, deep baking pan ready to pour the sauce in, once the caramel is done.
Place all the caramel sauce ingredients in a small saucepan and let them dissolve together over medium-high heat, without stirring. If sugar crystals form on the sides of the pan, brush the sides with a pastry brush dipped in a little water.
Now and then, gently swirl it around to lightly mix it. It will start turning color in approximately 8 to 10 minutes.
Once it reaches a dark amber color, remove from heat. Working quickly and carefully, pour enough caramel to thoroughly coat the bottom of the baking pan. Using kitchen gloves (pan will be hot), swirl around bottom and sides to coat evenly. Set aside to cool and harden.
Meanwhile, prepare the pumpkin pie flan: Place sweetened condensed milk, whole milk (or evaporated milk if you are using it instead), pumpkin, eggs, vanilla, and spice in a blender and cover tightly. Blend mixture well until smooth.
Skim off bubbles from the blender mixture and then gently pour the flan mixture through a fine sieve and into a separate, empty bowl.
Please, be careful when pouring to avoid creating bubbles. If necessary, use a spoon to help mixture pass through the sieve. Bits from the pumpkin purée and spices will be trapped on the sieve -- preventing them from interfering with the smoothness of the flan.
Skim off bubbles and pour mixture on top of hardened caramel (pie plate will be almost full). Place a large roasting pan in the preheated oven, position flan baking pan in the center of the roasting pan, and then, pour hot water into the large roasting pan to about halfway up the height of the flan pan.
Bake pumpkin pie flan 40-45 minutes, or until only slightly jiggly. NOTE: Mine was ready in 40 minutes!
Using kitchen gloves, remove flan from water and place on wire rack to cool completely.
Cover with aluminum foil and refrigerate for at least 2 hours to up to 2 days.
Before serving, run a thin knife gently around the edges, place a serving plate (one that can hold the caramel) on top of the flan pan, and invert the pan onto serving dish.
Pumpkin pie flan can be garnished on top with roasted pecan halves, if desired. Enjoy!