Hull and chop the strawberries, then combine them with 1/4 cup of the granulated sugar. Let the berries stand for 15–30 minutes, stirring once or twice, until they release plenty of juice.

Mash the macerated strawberries or briefly puree them. For a smoother ice cream, puree most or all of the fruit; for more texture, reserve some chopped berries and stir them into the mixture later.

In a large chilled bowl, whip the cold heavy cream with the remaining 1/4 cup sugar until firm peaks form. Stop mixing as soon as the cream holds its shape so it does not become grainy or overwhipped.

In a separate bowl, stir together the sweetened condensed milk, vanilla extract, fine salt, and strawberry mixture until evenly combined. If the strawberries are extremely watery, drain some excess juice before mixing.

Gently fold the condensed-milk mixture into the whipped cream in two or three additions. Use a wide spatula and fold just until combined so the whipped cream keeps as much volume as possible.

Transfer the ice cream mixture to a shallow, freezer-safe container, preferably a metal loaf pan or baking dish. Press plastic wrap or parchment directly against the surface, cover the container, and freeze for at least 6 hours; overnight is best.

Let the frozen ice cream stand at room temperature for 5–10 minutes before scooping. Serve in chilled bowls or cones, with fresh strawberry slices if desired.