In a large bowl, mix the pumpkin puree, pumpkin pie spice and vanilla extract until smooth.

In a separate chilled bowl, beat the cold heavy cream and ¼ cup sweetener with a hand mixer until stiff peaks form, about 2-3 minutes.

Gently fold the whipped cream into the pumpkin mixture in two or three batches with a spatula until just combined. Taste and add a little more spice or sweetener if needed.

Spoon the mousse into four glasses or bowls, cover with plastic wrap and refrigerate for at least 1 hour, until set.

For the caramelized pecans, melt the butter in a small skillet over medium heat. Add the pecan halves and 1 tablespoon sweetener and cook for about 5 minutes, stirring often, until the butter turns golden brown.

Spread the pecans out on parchment paper and let them harden for 10 minutes. Top each mousse with 4 pecan halves just before serving.