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Place the heavy cream in a medium mixing bowl and beat with an electric mixer on medium just until it begins to thicken.
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Gradually beat in the powdered sugar, then turn the speed to high and beat until stiff peaks form. (The peaks are stiff when you can pull the beaters out and the whipped cream holds its shape rather than collapsing on itself.)
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Place the mascarpone and vanilla in a large mixing bowl and stir a few times to combine and lighten the mascarpone. Gently fold the whipped cream into the mascarpone.
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Place the coffee and rum (if using) in a shallow bowl.
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Working with half of the Oreos, dip the top and bottom of each cookie in the coffee mixture. You don’t want them to be soggy; just make sure each cookie has absorbed a little of the liquid.
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Arrange the Oreos in one layer in the bottom of an 8-inch square baking dish. Break the cookies if necessary to completely cover the bottom of the dish. (Gaps between the cookies are fine but you don’t want large gaps around the edges.)
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Gently spread half of the whipped cream-mascarpone mixture over the cookie layer.
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Repeat the process with the remaining cookies, coffee, and whipped cream. Cover loosely with plastic wrap and refrigerate overnight.
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When ready to serve, top with cocoa powder or crushed Oreos; a sifter is helpful for dusting the cocoa powder in an even layer.
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Uneaten Oreo tiramisu can be stored, covered, in the fridge for up to 4 days. The cookies will continue to soften as the tiramisu sits but it will still be delicious.
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Oreo tiramisu can also be frozen for up to 2 months. Wrap it tightly (or store it in an airtight container) to prevent freezer burn. After freezing and thawing, the texture will be slightly softer and more mousse-like, but the flavor is still great.