Preheat the oven to 400°F. In a small baking dish, toss the strawberries with the butter and sugar. Using a paring knife, split the vanilla bean in half lengthwise. Using the back of your knife, scrape the seeds from the pod. Add to the strawberry mixture and toss to coat. Save the split pod for another use. Roast the strawberries until the fruit has collapsed and the juices are thick and syrupy, 30 to 35 minutes. Let cool completely.

When the strawberries are cool, scrape into a food processor or blender and puree until smooth. Strain through a fine mesh sieve set over a large measuring cup, pressing on the solids with a spatula. You should have about 1 cup of strawberry puree. Stir in the chopped fresh basil.

In a large bowl, whisk the strawberry puree with the sweetened condensed milk and salt.

In a medium bowl and using a hand mixer, beat the heavy cream on high speed until stiff peaks form, about 5 minutes.

Using a spatula, gently fold the whipped cream into the strawberry mixture. Scrape the ice cream base into a 9-by-5-inch metal loaf pan. Gently press a piece of plastic wrap onto the surface of the ice cream and wrap the entire pan tightly with more plastic wrap. Freeze for 2 hours.

Unwrap the ice cream and arrange the thinly sliced strawberries on the surface, if using. Cover with plastic wrap and return to the freezer until solid and scoopable, about 3 hours more or up to overnight. Let sit at room temperature for a few minutes before scooping.