In a medium sauce pan heat your half and half and sugar over a medium low heat until it is simmering. Then remove from heat.
In a bowl, whisk your eggs. Then temper them. To do this, slowly pour about half of your half and half mixture into your egg mixture, while whisking vigorously. Then slowly add your egg mixture back to your sauce pan with the remaining half and half mixture. While doing this whisk vigorously.
Add your heavy cream and mascarpone cheese.
Place pan back on the stove and heat over medium low heat continuously stirring until your cheese is melted. Continuously mix until your mixture as thickened enough that it coats the back of your spoon (about 30 minutes). Do NOT stop stirring or the bottom of your mixture will burn.
Then take it off of the stove and cool to room temperature for about an hour. Then place mixture into fridge for about 4 hours or overnight.
Pour mixture into ice cream mixer and churn until mixture has doubled in volume and it is thick fluffy and creamy looking (about 30 minutes).
Place half of your ice cream in a loaf pan. Then dollop about half of your jam mixture on top of that. Layer the rest of your ice cream on top and then add the remaining jam on top of that. Using a knife swirl together your ice cream and jam.
Place ice cream in the freezer and let it freeze overnight.
Serve and enjoy!