Prepare the jam first by quartering strawberries and heating in a medium pot with sugar and lemon juice. Cook on medium high until strawberries have cooked down to a syrup-jam consistency, about 20-30 minutes.
Cool jam completely.
To make the ice cream base, heat up cream and milk in a larger pot. In a separate bowl, whisk sugar and egg yolks together. When cream mixture is hot (do not boil), temper in egg yolks to bring the temperature of the eggs up slowly, then pour the egg yolk mixture back in the pot with the cream. Cook eggs in the cream until you can coat the back of a spoon or until the temperature reads 160 F (71 C).
Strain ice cream mixture into a big bowl fitted over an ice bath and cool down.
Once mixture is cold to the touch, add in lime zest and put in your ice cream maker to churn. Churn per your machine’s directions.
Put strawberry jam in a piping bag and cut off the tip.
Once ice cream is done, remove from your ice cream machine completely and pipe and fold strawberry jam. Place in an air tight container and freeze for 8+ hours.
Serve and enjoy! Stay cool friends!