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Combine the cream cheese and powdered sugar in a large mixing bowl and beat with an electric mixer on low to combined. Turn mixer to medium and beat until very smooth and creamy, 3 or 4 minutes.
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Scrape down the sides and bottom of the bowl, then beat in the mint extract, vanilla extract, and salt to combine.
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Turn mixer to low and gradually beat in the heavy cream.
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Once all the heavy cream has been added, gradually turn mixer to high and beat until the mixture is very stiff (basically, it should hold stiff peaks like whipped cream). This will take 5 to 10 minutes; stop the mixer a few times to scrape the sides and bottom of the bowl. (You really want to beat well here; whipping the cream is what helps the cheesecake hold its shape.)
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Use a rubber spatula to fold in the peppermint bark and mini chocolate chips.
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Scrape the mixture into the frozen crust, smooth the top, and cover loosely with plastic wrap. Refrigerate for at least 8 hours (or up to a couple of days).