In the bowl of a large stand mixer, cream the butter and the brown sugar until light and fluffy, about two minutes. Beat in the vanilla.
Slowly add the flour, scraping down the sides as necessary.
With the mixer still running, slowly add in the sweetened condensed milk. You may need to stop the mixer periodically to scrape down the sides. (DO NOT SCRAPE THE CAN WITH A SPATULA)
Once it is fully combined, stir in the chocolate chips.
Form the dough into one inch balls, and then shape into eggs. Place on a wax paper lined pan and cover loosely with plastic wrap. Refrigerate overnight.
Melt the candy melts according to the directions on the bag. Keeping the truffles in the refrigerator, and removing only three or four at a time, dip them in the candy melts one at a time with a fork. Gently tap off any excess chocolate and let dry on wax paper.