For the roasted pumpkin: Preheat a convection oven to 160°C/325°F.
Trim the stem off the top of the pumpkin. Cut it into quarters and remove the seeds.
Place the quarters on a sheet pan, flesh facing up.
Bake until the flesh is tender, about 20 minutes. It should yield to pressure easily when it is properly cooked.
Let it cool at room temperature. Scoop the flesh off of the skin and purée it in a blender until completely smooth. Discard the skin.
Weigh the necessary amount for the mousse and keep it at room temperature. This is important, since keeping it cold will have a negative effect on the gelatin when mixing the mousse ingredients together. The remaining amount can be frozen for further use.
For the pumpkin mousse: Lightly spray a sheet of Plexiglas or a very flat sheet pan with a fine mist of nonstick oil spray. Spread it evenly using a paper towel. Line the surface with a sheet of acetate and smooth it out with your hands using a clean paper towel.
Place 10 square molds onto the acetate-lined surface. These squares measure 9cm/3.5in by 9cm/3.5in long by 1.25cm/.5in deep; the corners are curved with a radius of 1.25cm/.5in.
Place this setup in a freezer to get the molds cold.
Whip the heavy cream with the first amount of sugar to medium-soft peaks. Reserve refrigerated.
Combine the egg yolks with the second amount of sugar in a bowl and stir constantly with a whisk over a hot water bath until they reach 57°C/135°F. Transfer to a mixer bowl and whip on high speed until it has quadrupled in volume and has cooled to room temperature.
Meanwhile, combine one-quarter of the purée with the gelatin in a bowl; place the bowl over a hot water bath and stir to dissolve the gelatin.
Once melted, combine this mix with the remaining pumpkin purée.
Mix the pumpkin purée with the pâte à bombe (egg yolk and sugar mixture) using a whisk.
Stir in one-quarter of the whipped cream using a whisk, then fold in half of the remaining whipped cream using a rubber spatula, and then fold in the remaining whipped cream until you obtain a smooth, homogenous mousse.
Transfer the mousse to a piping bag. Take the molds out of the freezer and have the shortbread bases available.
Pipe the mousse into the molds, starting with the corners. Keep the tip of the piping bag inside the mousse as you pipe to prevent air pockets from forming. Fill the molds about four-fifths of the way to the top. Place a shortbread square on top of the mousse and press down gently. The shortbread should be slightly higher than the border of the mold. This will help with moving the mousse; if it is completely flat it will certainly be damaged by handling. If there are empty gaps around the shortbread, fill them with more mousse. Even out the surface with an offset spatula. Cover the mousse with plastic and reserve in the freezer to harden.
Once they have hardened, unmold them. Line a full sheet pan with a nonstick rubber mat. Place a frozen mousse square on a spinning cake stand; gently and slowly spin it as you warm up the mold with a torch. Keep the torch a few inches away from the mold and make sure it is directly on the mold and not touching the mousse; otherwise it might melt. Gently slide the mold off the mousse and transfer the mousse to the prepared sheet pan.
Repeat with the remaining molds; make sure to space them evenly on the sheet pan. Return the molds to the freezer to harden again.
Meanwhile, make the pumpkin seed velvet spray and then spray the mousse.