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In food processor, pulse graham crackers into fine crumbs. Add melted butter and pulse a few times to combine into a texture that resembles wet sand.
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Open popsicle molds and divide the graham cracker mixture between them, pressing crumbs into four bottom sections of the molds. Place in the freezer to firm up, about 30 minutes.
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Place ice cream on the counter to soften 5 to 10 minutes, until very soft but not liquid.
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Fill ice cream molds with ice cream and return to the freezer overnight or for at least 5 hours.
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In microwave-safe bowl, melt chocolate in 10-second intervals, stirring between each interval. Stir in coconut oil.
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Pop the popsicles out of the molds and drizzle with chocolate mixture. Wait a few seconds for chocolate to harden, then enjoy.