Adjust oven rack to middle position and heat oven to 350 degrees. Spread nuts on an 18- by 12-inch rimmed baking sheet. Roast until fragrant and slightly darker in color, 12 to 15 minutes.

Meanwhile, microwave butter in a small bowl until melted; stir in rosemary, sugar, cayenne, and salt. Pour roasted nuts in a large bowl. Immediately add rosemary mixture and use a rubber spatula to make sure herb paste completely coats the nuts. Pour nuts back onto the cookie sheet and cool. Serve warm or at room temperature. (Can be stored in an airtight container up to 1 month.)