In medium bowl, sprinkle gelatin over cold water to soften; set aside.
In small saucepan, heat 1 cup of the evaporated milk to just boiling. Slowly stir hot milk into gelatin; stir until gelatin is dissolved. Mix in remaining evaporated milk, pumpkin puree, brown sugar, pumpkin pie spice, and vanilla; set aside.
Spray a 10-inch glass pie plate with non-stick vegetable coating. Pour mixture into pie plate; chill in the refrigerator until firm.