Preheat the oven to 325ºF. Line a baking sheet with parchment paper.
Add the almonds, cashews, walnuts and pistachios to the baking sheet.
Add the butter to a medium microwave-safe bowl. Microwave in 20-second increments until melted then whisk in the salt, brown sugar, cayenne pepper and rosemary.
Pour the butter mixture over the nuts and toss until well-combined. Arrange the nuts in a single layer on the baking sheet.
Bake the nuts for 10 minutes, stir, then bake them an additional 10 to 12 minutes until dark golden.
Remove the nuts from the oven and let them cool completely before serving.