Beat egg in a bowl. Stir in sweetened condensed milk, cinnamon, salt, nutmeg, and ginger.
Put water in a saucepan; sprinkle in gelatin, let stand 1 minute. Place saucepan over low heat; cook and stir until gelatin dissolves. Pour in milk mixture; increase heat to medium-low. Cook and stir until slightly thickened, 5 to 10 minutes. Remove from heat. Stir pumpkin in gently until combined.
Spread 3/4-inch layer of ice cream into crust; cover with pumpkin mixture. Freeze until set, about 2 hours.
