Chop the Toblerone chocolate into small pieces for easy incorporation into the ice cream.
In a medium bowl, combine the heavy cream, sweetened condensed milk, and vanilla extract. Whisk until smooth and well combined.
Stir in 80% of the chopped Toblerone chocolate, gently mixing to distribute it evenly throughout the ice cream base.
Pour the mixture into ice cream molds and insert the popsicle sticks. Freeze for at least 4-5 hours, or until solid.
Melt the dark chocolate in a double boiler or microwave in short intervals, stirring until smooth. Stir in the sunflower oil to create a thinner, more fluid consistency.
Dip the frozen ice cream bars into the melted chocolate, then immediately sprinkle with the remaining Toblerone pieces and almond slivers for added crunch.
Place the chocolate-covered ice cream bars on parchment paper and return them to the freezer for another 30 minutes to allow the chocolate to fully set.
Before serving, let the ice cream bars sit at room temperature for 2-3 minutes to soften slightly and make them easier to bite into.
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