Pour 1/4 cup (60 ml) of the cold milk into a small bowl. Sprinkle the gelatin powder evenly over the milk. Let it stand for 5 to 10 minutes to bloom, until it has absorbed the liquid and become thick.
While the gelatin blooms, combine the remaining 3/4 cup (180 ml) milk, heavy cream, pumpkin puree, brown sugar, pumpkin pie spice, and salt in a medium saucepan.
Whisk the mixture over medium-low heat until it is smooth and well combined.
Continue to heat, stirring occasionally, until the mixture comes to a gentle simmer. You will see small bubbles forming at the edges. Do not let it come to a full boil.
Remove the saucepan from the heat. Add the bloomed gelatin and vanilla extract to the hot pumpkin mixture.
Whisk for about 1 minute until the gelatin is completely dissolved and the mixture is uniform.
Carefully divide the warm mixture among 6 small glasses, ramekins, or custard cups.
Let the panna cotta cool at room temperature for about 20 minutes before transferring to the refrigerator.
Chill for at least 4 hours, or overnight, until firm to the touch but still has a slight jiggle.