Place a nonstick skillet on the stove and heat it over medium heat.
Add the walnuts, granulated sugar, brown sugar, and unsalted butter to the skillet. Stir gently so the butter melts and the sugar starts to coat the walnuts.
Keep stirring constantly for about 5 to 7 minutes. Watch closely as the sugar melts and the walnuts become evenly coated. Be careful not to burn them.
Immediately pour the walnuts onto a baking sheet lined with parchment paper. Use a spatula to separate any clumps before the coating hardens.
Let the candied walnuts cool completely. Once cool, serve as a snack or topping. Store in an airtight container.