In a large bowl, whip the cold heavy cream until medium-stiff peaks form.
Add the sweetened condensed milk and vanilla extract, then gently fold together, being careful not to deflate the whipped cream.
Stir in the strawberry puree until you have a uniform pink mixture.
Melt the dark chocolate in a double boiler or in the microwave, then stir in the coconut oil until smooth and glossy.
Line a loaf pan with parchment paper, then spread a layer of the strawberry ice cream mixture evenly across the bottom.
Pour a thin layer of melted chocolate over the ice cream layer, and place in the freezer for 10 minutes to harden.
Repeat the layering process until all of the ice cream mixture and chocolate have been used. Ensure the top layer is chocolate.
Freeze for at least 4 hours, or preferably overnight, until completely firm.
Before serving, let it stand at room temperature for a few minutes, then slice and garnish with fresh strawberries and white chocolate shavings.
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