Use a mixer and a large bowl to combine the softened butter, confectioners’ sugar, sweetened condensed milk, and vanilla, then fold in the coconut and toasted pecans. The filling should look evenly mixed, with coconut and nuts distributed throughout the soft mixture.
Separate the filling into two portions, cover them, and refrigerate for 1 hour. The chilled mixture should feel firmer and scoopable rather than loose.
Keep one portion refrigerated while rolling the other into 1-inch balls on waxed paper-lined baking sheets, then repeat with the remaining portion and refrigerate the shaped centers for 30 minutes longer. The balls should hold their rounded shape without slumping.
Gently heat the chocolate chips and shortening in a double boiler or metal bowl over barely simmering water, stirring as they melt. The coating is ready when it looks smooth and flows easily from the spoon.
Coat each chilled ball in melted chocolate, let the excess drain, and transfer it back to the waxed paper, adding extra coconut on top if desired. A thin, even coating should cover the center without leaving a large puddle underneath.
Refrigerate the coated candies until the shells set, then keep them refrigerated in an airtight container. The finished chocolate should feel firm rather than wet or tacky.