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Set 4 martini glasses or shallow dessert bowls in the freezer. In a small cup, sprinkle the gelatin over 1 tablespoon of cold water and let stand until softened, about 3 minutes. Fill a medium bowl half full of ice water.
In a small saucepan, combine 1/4 cup of the sugar with 2 tablespoons of water and simmer over moderate heat just until the sugar is dissolved. Remove the sugar syrup from the heat and whisk in the softened gelatin until dissolved. Stir in the lime juice and 1/2 teaspoon of the lime zest. Set the saucepan in the ice water bath and stir the gelée until cooled. Pour the gelée into the chilled glasses and freeze until firm, about 15 minutes.
Meanwhile, in a medium saucepan, combine 1 cup of the strawberries with 2 tablespoons of sugar and 1/4 cup of water and bring to a boil. Let cool slightly. Transfer the strawberry mixture to a blender and puree until smooth. Pour the puree into a bowl and stir in the remaining strawberries and half of the vanilla bean seeds; let cool.
In a medium bowl, whisk the heavy cream with the remaining 2 tablespoons of sugar, 1/2 teaspoon of lime zest and vanilla bean seeds until soft peaks form. Spoon the strawberry puree over the lime gelée. Top the strawberry puree with a scoop of vanilla ice cream and a dollop of the whipped cream and serve immediately.