Bring half and half and whipping cream to a simmer over medium low heat in a medium-heavy saucepan.
In a separate, medium size bowl, whisk egg yolks and sugar together.
When cream is heated, whisk hot cream into egg yolk mixture in a slow, steady drizzle. Return mixture to saucepan and return to stove. Stir continuously over medium-low heat until mixture thickens and coats the back of a spoon. Do not boil.
Remove from heat and stir in 3/4-cup Black Raspberry Jam or Sour Cherry Jam until melted.
Cover with plastic wrap, setting the wrap directly onto the custard and chill. Freeze in an ice cream maker according to manufacturer's directions.