Preheat the oven to 350° F/175° C.

CUSTARD: In the mixing bowl, beat the pureed pumpkin, eggs, half & half, brown sugar, salt, and cinnamon, ginger, allspice, and nutmeg until thoroughly combined. Pour the mixture into the prepared 9×9 pan. Bake until the center is slightly wobbly and the edges are firm, about 50 to 60 minutes. Remove from the oven and cool on a rack, then chill in the refrigerator until it is completely cold, at least 1 to 2 hours.

CREAM: While the custard bakes, beat together the mascarpone, cream, and sugar together with a mixer until the mixture holds stiff peaks. Cover and refrigerate until ready to serve.

ASSEMBLE: In the bottom of each glass, spoon in about 3 tablespoons of the chilled custard, then top off with a dollop of the cream. Sprinkle on some of the gingersnap crumbs and serve.