Bloom the gelatin. Put the 75 g (5 tbsp) of cold water in a small bowl and sprinkle the 14 g (½ oz, 2 envelopes) of unflavored gelatin evenly over the top. Leave it untouched for 10 minutes, until it looks like a firm sponge.
Beat the cream cheese. In a large bowl, beat the 600 g (21 oz) of cream cheese with a mixer on medium speed for 1 to 2 minutes, until smooth and glossy.
Add the sugar. Add the 100 g (½ cup) of sugar in two batches, beating 30 seconds after each, until there are no lumps.
Pumpkin and spices. Add the 500 g (2 cups) of cold puree, 8 g (1 tbsp) of cinnamon, 3 g (½ tsp) of salt, and, if using, the vanilla, ginger, nutmeg, cloves, and turmeric. Mix the turmeric with the other spices in a small bowl first, or it will leave yellow specks. Beat on low only until the color is even, 40 to 50 seconds, no more.
Whip the cream very lightly. Whip the 300 g (1¼ cups) of heavy cream only until it falls from the beaters in a slightly thick ribbon. Here it is better to under-whip than over-whip: at stiff peaks it breaks when you fold it in and leaves lumps of butter.
Melt and temper the gelatin. Melt the bloomed gelatin for 12 to 15 seconds in the microwave, or over a water bath while stirring, until liquid and clear. Do not let it boil: above 80 °C (175 °F) it loses its setting power. Stir 3 tablespoons of the pumpkin filling into the gelatin bowl quickly, to even out the temperatures.
Add it without stopping. Pour the tempered mixture into the filling and beat on low for 20 seconds, without pausing to do anything else: the gelatin starts to set as soon as it touches the cold filling.
Fold in the cream. With a silicone spatula, gently: down through the middle, across the bottom, up the side, and give the bowl a quarter turn. Repeat until you see no white streaks, and stop there.