Preheat oven to 350°F. Line rimmed baking sheet with foil; brush generously with vegetable oil. Toss nuts, toffee bits, sugar, and 1/8 tsp salt in medium bowl to blend. Add butter and toss to coat. Place mixture in center of prepared sheet; pat to single layer. Bake until toffee bits are soft (but retain shape), about 15 minutes. Cool crunch completely on sheet. Transfer to work surface; chop coarsely.
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Whisk 3/4 cup whipping cream, sugar, and egg yolks in heavy medium saucepan to blend. Stir over medium-low heat until thickened to pudding consistency, about 10 minutes (do not boil). Transfer mixture to large bowl. Mix in pumpkin, rum, vanilla, ground cinnamon, ginger, nutmeg, 1/4 tsp salt, and allspice. Refrigerate uncovered until cold, stirring occasionally, about 40 minutes.
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In each of 4 medium (10-ounce) goblets, layer 1/3 cup mousse and generous tablespoon crunch. Repeat 2 more times (some crunch may be left). If necessary, whisk reserved 1/2 cup whipped cream to soft peaks. Pipe or drop dollop of cream onto mousse in each goblet. Cover; freeze overnight. (Can be made 2 days ahead. Keep frozen. Let stand at room temperature 30 minutes before serving.)
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