Step 1

Combine the heavy cream, yogurt, sugar, syrup, salt and vanilla in a bowl and whisk well to combine and dissolve the sugar.

Step 2

Refrigerate or chill the mixture over an ice bath until it is very cold.

Step 3

Transfer the mixture to a pre-chilled ice cream maker and churn into frozen yogurt.

Step 4

Stir each jam to loosen it up a little. Spread half of the frozen yogurt into a 4-cup rectangular container. Dollop two small spoonfuls of peach jam and two small spoonfuls of blackberry jam over the yogurt. Using a knife or wooden skewer, swirl the jam into the yogurt. Repeat with another layer of the yogurt and the jams. Cover tightly and freeze for at least 2 hours before serving.