In a food processor, puree the raspberries until smooth. Strain the raspberry puree through a fine-mesh sieve to remove the seeds. Discard the seeds.
In a large bowl, beat the heavy cream with an electric mixer until soft peaks form. Gradually add the powdered sugar and vanilla extract and continue beating until stiff peaks form.
Gently fold the raspberry puree into the whipped cream until just combined. Be careful not to overmix.
Spoon the mousse into serving glasses or bowls. Cover and refrigerate for at least 2 hours to allow the mousse to set.
Garnish with fresh raspberries before serving.
Notes
For a richer flavor, add a tablespoon of raspberry liqueur to the puree.