Combine heavy cream, whole milk, 3/4 cup granulated sugar, and a pinch of salt in a medium saucepan. Heat over medium-low heat, stirring occasionally, just until the sugar dissolves completely. Do not boil. Remove from heat.

Stir in the vanilla extract. Pour the mixture into a large bowl, cover with plastic wrap, and refrigerate for at least 4 hours, or preferably overnight, until thoroughly chilled. This step is crucial for creamy ice cream.

For the strawberry swirl: Combine hulled and quartered strawberries, 1 tbsp granulated sugar, and 1/2 tsp lemon juice in a blender or food processor. Blend until smooth. For a very smooth puree, strain through a fine-mesh sieve to remove seeds, if desired. Set aside.

For the mango swirl: Combine peeled and diced mango, 1 tbsp granulated sugar, and 1/2 tsp lemon juice in a blender or food processor. Blend until smooth. Set aside.

Once the ice cream base is thoroughly chilled, pour it into your ice cream maker and churn according to the manufacturer's instructions. This typically takes 20-25 minutes, until the ice cream is thick and resembles soft-serve.

Transfer about half of the churned ice cream to an airtight freezer container. Drizzle generously with half of the strawberry puree and half of the mango puree. Using a knife or spoon, gently swirl the purees into the ice cream, being careful not to overmix.

Add the remaining ice cream to the container, then drizzle with the rest of the strawberry and mango purees. Swirl again. Smooth the top.

Cover the container tightly and freeze for at least 6 hours, or until firm, before serving. For best results, allow it to freeze overnight.