Melt the butter in a non-stick skillet over medium heat. Place a sheet of parchment paper or a silicone mat next to the stove. Add the walnuts and sugar. Stir with a rubber spatula to combine.
Continue stirring until the sugar melts and the walnuts are well-coated, about a minute longer. Quickly transfer the walnuts to the parchment and work quickly with a spatula to spread them out to avoid clumping.
Notes
Candied walnuts can be stored in an airtight container at room temperature for up to a month.