Place milk, 1 cup of cream, ½ cup sugar, and salt in a medium sauce pan. Heat until the mixture is steaming, but not boiling.
Remove from heat. Whisk egg yolks in a medium bowl until combined. Very slowly whisk in warm milk. Transfer mixture back to saucepan and set over medium heat. Stir constantly until mixture begins to slightly thicken and is 170 degrees. Mixture should coat the back of the spatula. Remove from heat immediately so the mixture doesn't scramble.
Place remaining ¾ cup heavy cream in a large bowl and place strainer over bowl. Pour thickened yolk mixture through strainer to remove lumps. Stir with cream.
Chill mixture until completely cold, about 4-6 hours. Once chilled, add pureed strawberries and stir together. Ice cream base is now ready for your machine. Freeze ice cream according to machine instructions.
Once mixture is ready, scoop into storage container and cover with plastic wrap. Freeze ice cream until solid, about 8 hours.