In the bowl of an electric mixer fitted with the paddle attachment, mix the egg, egg yolks, and 1/2 cup of the sugar together on low speed until just combined. Meanwhile, scald the cream in a small saucepan until it's very hot to the touch but not boiled. Add the cardamom and mix well. With the mixer on low speed, slowly add the cream to the eggs. Add the framboise and vanilla. Distribute the raspberries among 6 (6 to 8 - ounce) ramekins and then pour the custard mixture into the ramekins until they're almost full. (I use a large glass measuring cup for easy pouring.)
Place the ramekins on a sheet pan and carefully pour hottest tap water into the pan to come halfway up the sides of the ramekins. Bake for 35 to 40 minutes, until the custards are just set when gently shaken. Remove the custards from the water bath, cool to room temperature, cover and refrigerate until cold.
To serve, spread 1 tablespoon of sugar evenly on the top of each ramekin and heat with a kitchen blowtorch until the sugar caramelizes evenly. Allow to sit at room temperature for a minute until the caramelized sugar hardens.