We made this flan in a 4-cup-capacity savarin mold, but a 9-by-2-inch round cake pan or a 9-inch glass pie plate can be used as well.
Preheat oven to 450 degrees. Place sweet potatoes on a baking sheet, and roast until very soft, about 1 hour. Allow to cool. Peel off skin, and discard. Place sweet potatoes in the bowl of a food processor, and puree until completely smooth. Measure 1 1/2 cups puree, reserving any excess for another use. This step may be done a day in advance.
Reduce oven to 325 degrees. Combine 1 cup sugar and the water in a small saucepan, and cook over medium heat. Cook, stirring occasionally, until sugar dissolves. Brush down sides of pan with a pastry brush dipped in water to prevent crystallization. Increase heat to medium-high; boil, without stirring, until the syrup turns a deep amber, 5 to 6 minutes. Pour caramel into savarin mold or a 9-by-2-inch round cake pan. Holding the pan with pot holders, swirl to coat bottom and halfway up sides of dish.
In a large bowl, combine sweet-potato puree, remaining 3/4 cup sugar, allspice, cinnamon, salt, eggs, and egg yolks. Mix in vanilla and scalded milk, then pass the mixture through a fine sieve. Pour into caramel-lined pan, and cover with foil. Set in a roasting pan, and pour boiling water into the roasting pan halfway up sides of flan dish.
Bake for 50 to 55 minutes, or until center of flan is nearly set: A thin-bladed knife inserted in the center should come out clean. Let cool to room temperature, and place in the refrigerator to chill overnight.
To unmold, run a sharp knife carefully around flan, and cover with a serving plate; invert quickly. Remove pan; serve.