In a medium saucepan stir together the cream, milk, and sugar. Heat over medium heat until sugar is dissolved and mixture is just starting to simmer. Do not allow to boil. Whisk the egg yolks lightly in a small bowl; gradually whisk in about 1 cup of the milk mixture. Pour the egg yolk mixture back into the saucepan. Cook, stirring constantly, over medium heat for 6 to 8 minutes or until mixture thickens and coats the back of a metal spoon. Remove from heat and stir in vanilla. Immediately place in a large bowl of ice water and stir for 2 minutes to cool slightly. Add lavender sprigs. Transfer to a storage container; cover and chill overnight.
Strain the custard mixture through a fine mesh sieve; discard solids. Freeze in a 2-quart ice cream freezer according to manufacturer's directions. Gently stir in strawberry jam to form a swirl. Transfer to an airtight storage container and freeze for 4 hours before serving.