To begin, place your heavy saucepan on the stove over medium heat. Allow it to warm up a bit, and then add in the butter. Let it melt and become slightly brown – butter that has been browned will always have more flavour, as compared to butter that is taken off the heat immediately after it melts.
Next, crack the egg open, and separate the yolk from the whites. Add the yolk to the melted butter on the stove, and follow it up by pouring in the can of condensed milk. Keep stirring the mixture constantly, and wait for it to reach a boil.
Once the mixture boils, take it off the heat, and place it on an even, heat-proof surface. Add in the coconut and the pecans, and stir them in thoroughly, until the frosting thickens just a little. Allow it to cool until it reaches room temperature, and once it does, your coconut pecan frosting is ready for use.