• Pre-heat the oven to 350°F. Slice the strawberries in half and spread them out on a rimmed baking sheet. Sprinkle a tablespoon of sugar over them. Place the strawberries in the oven for 45 to 60 minutes.
• Scrape the roasted strawberries into a food processor or blender and puree until smooth. Set aside while you prepare the rest of the ingredients. 
• Pour the milk into a medium saucepan and heat it over medium heat until it just starts to get small bubbles but does not boil. After the milk gets hot, remove it from the heat and stir in the basil leaves then place a lid on it and let it sit for 1 to 2 hours. (the longer you let it sit, the more basil flavor.)
• Place the saucepan back on the stove and add the cream, goat cheese, 3/4 cup of sugar, and salt to the basil/milk mixture. Cook over medium heat, stirring until the mixture is warm and the goat cheese melts.
• In a separate bowl beat the yolks with the remaining 1/4 cup sugar.
• Whisk a cup of the warm milk mixture into the yolk mixture. Continue whisking until well combined then pour it into the saucepan with the rest of the warm milk mixture. 
• Stir the mixture constantly while you heat it over medium heat. Continue heating and stirring until an instant-read thermometer reads 180°-185°F. (make sure the mixture does not boil).
• Pour the custard into the strainer that is set over a bowl to remove any bits of cooked egg yolk and the basil leaves.  
• Stir in the vanilla and the strawberry puree then cover the mixture and place it in the fridge to chill. 

Ice cream machine:

• Pour the custard into an ice cream maker and follow the manufactures instructions for churning ice cream. 
• Transfer the ice cream to an airtight container and freeze for 3 to 4 hours