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Spread the ice cream into the bottom of the crust and freeze until firm, 1 hour.
For the lemon curd: Combine the milk and 1/4 cup water in a medium saucepan over medium heat. Mix together the sugar, cornstarch, salt and yolks in a large mixing bowl. When the milk is hot, but not boiling, slowly pour into the yolk mixture while whisking vigorously. Once both mixtures are combined, pour all ingredients back into the saucepan. Add lemon juice and cook over medium heat, stirring constantly until thick and boiling. Pour through a fine mesh sieve into a medium bowl, and fold in the butter until combined. Cool until set and at room temperature, 2 to 3 hours.
For assembly: Pour the cooled lemon curd into the pie shell over the ice cream layer. Freeze until firm, 1 to 3 hours. Top with the raspberry compote just before serving.