For the dairy-free ice cream, which gets its aromatic brightness from key limes and richness from avocado and coconut milk, be sure to use a coconut milk that contains only coconut, water, and guar gum. Added ingredients will prevent the coconut milk from separating.
Squeeze the avocado flesh into a high-powered blender. Add the sweetened condensed milk, Key lime juice and zest, salt, and vanilla. Blend on high until smooth.
Open the cans of coconut milk, and loosen the firm cream from the edges of the cans. Place the firm cream in the bowl of a stand mixer fitted with a whisk attachment. Beat on high until thick and smooth, about 3 minutes. Slowly drizzle in the avocado mixture, beating until completely incorporated.
Line a 9×9-inch cake pan with foil. Arrange 6 rectangular graham crackers in the bottom of the pan, cutting to fit to cover the bottom completely. Pour half the avocado mixture over in an even layer, using a rubber spatula to smooth to the edges. Layer with 6 more graham crackers, the remaining avocado mixture, and the remaining 6 graham crackers. Cover and freeze for at least 4 hours until firm.
Remove from the freezer, and using the edges of the foil, lift the bars out of the pan. Cut into 9 squares, place on a baking sheet, and refreeze.
In a large, very clean metal or glass bowl, add only the liquid from the can of chickpeas (save the chickpeas for another use) and the Key lime juice. Beat with an electric mixer on medium speed until frothy. Increase the speed to high and beat, slowly adding the sugar, until stiff peaks form, 4 to 5 minutes.
Immediately remove the bars from the freezer, and top each with a dollop of meringue. Using a kitchen torch, toast the meringue just until set and charred along the edges. Let bars stand about 5 minutes before serving.
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