Heat a medium saucepan over medium high heat. Add the strawberries and sugar. Bring to a boil (the berries will release liquid and the sugar will melt, making a sauce).
Reduce heat to medium and simmer for 10 minutes for the strawberries to soften. Mash as much or little as you wish with a potato masher or fork. Set aside and let cool to room temperature. (I like to leave it a little chunky so I get pieces of strawberries in the ice cream).
Put the heavy cream in a stand mixer and mix on medium high until stiff peaks form, approximately 2 minutes.
Meanwhile, combine the sweetened condensed milk, vanilla, salt, and chopped basil in a small bowl. Stir to combine.
Once the cream is whipped, add a cup to the sweetened condensed milk mixture and fold or gently stir until combined. Add that mixture back into the rest of the whipped cream and fold to combine.
For a strawberry swirl: Pour the whipped cream mixture into a 9 by 5 loaf pan. Add the strawberry mixture in clumps and drag a knife or spatula through the mix to make strawberry streaks.
For a mixed ice cream with no streaks: Gently mix the strawberry mixture into the cream mixture until combined. Pour the ice cream into a 9 by 5 inch loaf pan.
Cover the pan and freeze until fully set, approximately 5 hours or more.
The strawberries will turn the ice cream a very pale pink. If you want a deeper pink, add a couple drops of red food coloring to the milk mixture in step 4.