Combine milk, sugar, cocoa powder, corn syrup and salt in a medium saucepan over low heat, whisking until sugar has dissolved.
Remove mixture from heat and stir in vanilla.
Cool mixture to room temperature by placing the pan in a bowl of ice water and stirring occasionally. (Be careful that the ice water doesn't overflow into the pan.)
Add about 2 tablespoons of strawberries to each of the popsicle molds, and then top with the milk mixture. Freeze for 1 hour, insert the popsicle sticks, and then continue freezing until solid, about 24 hours.
When ready to serve, run warm water over the molds to release fudgesicles.
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