Toss the strawberries in the balsamic vinegar and sugar and let sit for 20 minutes. Pour the mixture on a baking pan covered in foil folded up on the sides to capture the juices. Roast the strawberries in a preheated 425F oven until they start to caramelize, about 15-20 minutes. Place the strawberries and the juices into a container and chill in the fridge.
Mix sugar and egg yolks in a cup and stir until sugar dissolves. Heat the cream and milk in a sauce pan until it almost boils, about 5 minutes. Reduce the heat to low. Add one tablespoon of the cream mixture to the eggs to temper them, then add a couple more tablespoons. Add the egg mixture to the sauce pan and stir to mix. Cook at low heat until it thickens and can coat the back of a spoon, being careful not to overcook. Strain custard into a bowl set over ice water, stir and cool. Chill the mixture in the fridge for 4 hours or overnight.
Add the strawberry and tablespoon of vodka to the custard. Freeze according to the instructions of your ice cream machine.
Recipe adapted from Closetcooking.com