Over medium heat melt butter in saucepan, then stir in flour. Cook flour for 30 seconds, then slowly add in milk a bit at a time, stirring constantly until smooth and lump free.
Add in brown sugar, cocoa and salt and bring to a boil. Continue stirring for 2 more minutes until mixture is thickened.
Remove from heat and add vanilla. Cool for 20 minutes, stirring often.
Pour into popsicle molds and freeze until firm.
Did You Know - Silicone and stainless steel popsicle molds are the best to use since their surface (microscopically) is completely smooth, so the popsicles' slip out with hardly any effort. If you could look at the surface of plastic under a microscope you would see it covered in peaks and valleys. This is why you need to use a lot of hot water to melt the popsicle to get it out, since it gets stuck in the bumpy surface of plastic mold.
You can always freeze chocolate milk into popsicles, but for a creamy Fudgesicle-like treat, try this!