In a medium saucepan, before turning on the stove, mix together the brown sugar, cocoa, and cornstarch.
Slowly add in 1/2 cup of milk and whisk until the mixture is smooth.
Place the pan over medium heat, and stir continuously while adding in the remaining milk.
Once the mixture has started to thicken (about 7-10 min), turn off the stove and remove the pan from the heat while still stirring. Let the chocolate mixture cool for a few minutes.
Transfer the chocolate mixture into a spouted measuring cup. (This will make pouring it easier.) Then fill the popsicle molds almost to the top. Insert the sticks or mold tops and freeze for 6 hours or overnight.
When your ready to eat, take out a fudgesicle and enjoy! If you have any trouble getting the pops to release from the mold, run the bottom of the mold under warm water just until the pop releases.