Beat heavy whipping cream in a large bowl with a mixer until stiff peaks form. Fold in sweetened condensed milk and vanilla extract.
Divide ice cream mixture into three separate bowls. In one bowl, mix in cocoa powder until evenly combined. In another bowl, mix in mashed strawberries until evenly combined. Leave the last bowl vanilla.
Pour all three ice cream mixtures into a large freezer safe container. Cover and freeze for at least 4 hours.