Preheat the oven to 320°F (160°C), or 285°F (140°C) for a fan-assisted oven. Position a rack in the center.
Arrange the strawberries on a large baking tray. Sprinkle with sugar and gently toss until coated, then spread the berries into an even layer.
Roast for 45 minutes, rotating the tray halfway through cooking.
Remove the tray and gently toss the strawberries. Return them to the oven for approximately 15 minutes. Watch carefully toward the end so the concentrated strawberry juices don't burn or become overly sticky.
Scrape the roasted strawberries, juices, and caramelized bits into a food processor or blender.
Blend until as smooth as possible. Transfer the strawberry puree to a bowl and allow it to cool completely.
Add the sweetened condensed milk and vanilla extract to the cooled strawberry puree. Beat on high speed for approximately 1 1/2 minutes until well combined and slightly aerated.
Pour the cold whipping cream into a separate large bowl. Beat with an electric mixer on high speed until stiff peaks form, approximately 3 minutes. Avoid overbeating.
Add a generous spoonful of whipped cream to the strawberry mixture. Fold gently until mostly incorporated.
Add another spoonful of whipped cream and fold several more times.
Pour the strawberry mixture into the remaining whipped cream. Gently fold until the mixture is an even pale pink. A few visible streaks are fine, so avoid excessive mixing.
Transfer the Strawberry Ice Cream mixture to a freezer-safe container and smooth the surface.
Place a sheet of parchment or baking paper directly against the surface of the ice cream, gently pressing out trapped air. Cover tightly with a lid.
Freeze for at least 12 hours, preferably overnight, until completely firm.
Before serving, remove the ice cream from the freezer and let it sit briefly at room temperature if needed for easier scooping. Serve in bowls or ice cream cones.