In a large bowl, combine the egg yolks and whisk to combine. In a large saucepan combine the milk, sugar and corn syrup. Heat over medium heat until the milk simmers and the sugar and corn syrup have dissolved. . Remove from the heat Slowly drizzle some of the hot milk into the egg yolks, whisking the egg yolks constantly. Continue to add the milk to the eggs. Pour the egg and milk mixture back into the saucepan and place over medium heat. Cook until the mixture thickens and can coat the back of a spoon. Remove saucepan from heat and chill mixture for 4 hours or overnight.
Pre heat the oven to 300 degrees. Line a sheet pan with parchment paper. Toss the strawberries with the balsamic vinegar and spread on the sheet pan. Roast in the oven for 20 minutes or until the stawberries are tender and and the balsamic vinegar has evaporated. Remove from the oven and cool.
Fill your ice cream maker with the cold milk/egg custard and churn according the the manufacturers instructions. Either add the strawberries to the mixture in the last minute or so of churning or layer it into the container you are going to store/freeze the sherbet in.
Freeze sherbet for about 1 hour before eating.
Notes
When frozen the sherbet will be much harder than ice cream - let it sit out for about 5 - 10 minutes to soften so you can scoop it!