1. Preheat oven to 375 degrees F. Line a rimmed baking sheet with parchment paper.
2. In a medium bowl, combine trimmed and sliced strawberries, 2 tablespoons of the sugar, the vanilla extract, and the salt. Spread out onto prepared baking sheet and roast for 25-30 minutes.
3. Remove the pan from the oven and carefully transfer the strawberries and accumulated liquid to your blender. Allow to cool for about 10 minutes.
4. Add 2 more tablespoons of sugar to the blender, along with the juice of one lime (or lemon) and the basil. Add ice cubes and process until fairly smooth (it's fine for some ice chunks to remain). Taste and add more lime (or lemon) juice, sugar, and/or more ice, as desired.
5. Pour into glasses (over additional ice if you like) and serve immediately...I got 2 servings that were 2 cups each out of this recipe.