Chill the mixing bowls and beaters in the refrigerator for 10 minutes. Pour the heavy cream into a large chilled bowl. Using a hand or stand mixer, whip the cream on medium-high speed until stiff peaks form, about 3-4 minutes. The whipped cream should hold firm when lifted.
Add the sweetened condensed milk and vanilla extract to the whipped cream. Gently fold together using a spatula until well combined, maintaining the airy texture. The mixture should be smooth and uniform.
Divide the mixture evenly into three separate bowls. In the first bowl, fold in the blueberry puree until fully incorporated, creating a vibrant blue mixture. In the second bowl, fold in the strawberry puree for a bright red color. Leave the third bowl plain for the white layer.
Pour the white mixture into a freezer-safe container, spreading evenly. Add dollops of the red and blue mixtures over the white layer in a streaked or swirled pattern to create a patriotic visual effect. Use a toothpick or knife to gently swirl the layers without fully blending them, creating a marbled appearance.
Cover the container with plastic wrap or a lid. Freeze the mixture for at least 6 hours or until firm. During freezing, occasionally scrape and stir the mixture if using a shallow dish to prevent ice crystals and ensure a smooth texture.
Remove the ice cream from the freezer 5 minutes before serving. Scoop into bowls or cones, display the colorful layers, and serve immediately. The final texture should be creamy, firm, and visually striking with distinct red, white, and blue swirls.
