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To make the toasted marshmallow whipped cream: In a large bowl or the bowl of a stand mixer, whip the cream, confectioners’ sugar, vanilla bean paste, and salt to soft peaks, about 3 to 4 minutes at medium-low speed.
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Place the mini marshmallows on a lightly greased baking sheet and broil on low for 30 to 90 seconds, until deep golden brown all over with some charred spots. This happens very quickly, so keep a close eye on the marshmallows and do not walk away from the oven. Mini marshmallows can also be toasted with a blow torch or roasted over a fire until toasted all over and charred in spots.
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Remove the mini marshmallows from the oven and allow them to cool for 2 to 4 minutes. Once the toasted mini marshmallows are cool enough to handle but still slightly warm, transfer them to the bowl of whipped cream. (A small offset spatula or a bowl scraper are helpful tools here.)
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Whip the cream and marshmallows at low speed until the marshmallows have broken down slightly, then increase the speed to medium and whip until medium peaks form, 1 to 2 minutes.
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To assemble the s’mores icebox cake: Line a 9" x 4" loaf pan with plastic wrap so that there are several inches of excess overhang on all sides. (See "tips" below for alternative pan options.)
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Use a flexible spatula to portion about 1 cup (120g) of the whipped cream into the bottom of the loaf pan. (If using a muffin scoop, you'll need about 4 level scoops.) Use a small offset spatula or the back of a spoon to smooth the cream into an even layer about 1/2" thick. Arrange the graham crackers in a single layer on top of the cream, breaking them up as needed to fit from edge to edge; if you’ve made homemade graham crackers cut into 3 1/2" x 1 1/2" rectangles, you should be able to fit 6 crackers neatly in a single layer.
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Portion a scant 1/4 cup (about 50g) of chocolate sauce on top of the graham crackers and spread it into a thin, even layer.
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Add another 1 cup (120g) of the whipped cream, spread it into an even layer, then add another layer of graham crackers, followed by another layer of chocolate sauce. Repeat this layering process — whipped cream, graham crackers, chocolate sauce — until you’ve used all the toasted marshmallow whipped cream and are nearing the top of the pan. There will be leftover graham crackers and chocolate sauce; save these for the garnish.
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Cover the icebox cake with the overhanging plastic wrap and chill, in the pan, for at least 24 hours in the refrigerator, which will give the graham crackers a chance to soften and transform into a cake-like texture.
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To serve: Remove the cake from the refrigerator, uncover the icebox cake, invert it onto a cutting board or serving plate, and gently remove the plastic wrap. If you’re a perfectionist, use an offset spatula or bench knife that’s been run under hot water and then dried to smooth out the whipped cream and cover any exposed layers.
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To garnish: Use the leftover chocolate sauce and graham crackers (broken into small pieces or crushed into crumbs) to garnish the top of the icebox cake, if desired. Additional toasted marshmallows can also be used. For the neatest slices, use a sharp chef knife that’s been run under hot water and then dried to cut the cake; serve immediately.
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Storage information: Store leftover icebox cake, covered, in the refrigerator for up to 3 days.