In a small pot on the stove top, heat milk and vanilla over medium heat until hot, but not boiling. It will just about start to simmer when it's hot enough.
While the milk is heating, in a medium to large bowl, beat egg yolks, sugar, and arrowroot powder until it's very pale in color. This should only take a minute or so.
Once the milk is ready, pour a small amount (⅛-¼ cup) of the hot milk into the egg yolk mixture while whisking. Once it's incorporated, pour the egg yolk mixture into the pot of milk while whisking. Then whisk frequently over low heat until you feel the mixture thicken. This should take only a few minutes.
Take off the heat and pour into a bowl. Put siran wrap right onto the mixture so a skin doesn't form and refrigerate at least 4 hours or overnight. It should be cold to the touch.*
The next day, take the mixture out of the fridge and mix with a whisk or immersion blender until smooth. Measure out 1 cup of strawberry jam and blitz with an immersion blender until smooth. Mix together the strawberry jam and custard mixture.
Pour into the ice cream bowl and churn with ice cream maker for about 20-30 minutes. Scoop out of the ice cream maker into chilled container and swirl in remaining ¼-½ cup of strawberry jam depending on how much you want. Place in the freezer for a couple of hours before serving.
*At this point, if your ice cream maker requires it, you should put the ice cream bowl in the freezer overnight. You should also put the container you plan to put your finished ice cream in, in the freezer as well.