Place the cream cheese in a stand mixer fitted with the paddle attachment. Mix the cream cheese on medium speed until creamy and smooth. While the mixer is running, gradually add the sugar and salt. Blend until incorporated. Add the mascarpone and mix until combined. Slowly add the milk and vanilla. Remove the paddle attachment and gently fold in the Greek yogurt with a spatula. Cover and refrigerate overnight.
Process according to your ice cream maker directions. Transfer to a freezer safe container and freeze for several hours before serving.
For the Sauce:
Place the blackberries, sugar and salt in a medium saucepan. Cook until the berries are very soft and the sugar is dissolved. Pour the blackberry mixture into a blender and process until smooth. Pour the mixture through a fine strainer over a bowl. Add the framboise and lemon juice. Refrigerate until ready to serve.
Notes
Recipe for ice cream adapted from a Cuisinart recipe.
Ice cream makes about 5 cups.
Recipe for the sauce adapted from a recipe by Bobby Flay.
Nutrition information is calculated using an ingredient database and should be considered an estimate. When multiple ingredient alternatives are given, the first listed is calculated for nutrition. Garnishes and optional ingredients are not included.