Preheat oven to 350°. Toss almonds, pecans, walnuts, pumpkin seeds, brown sugar, maple vinegar, oil, spice rub, and salt in a medium bowl to evenly coat nuts. Transfer to a rimmed baking sheet or a large cast-iron pan and roast, tossing occasionally, until nuts are toasted and brown sugar caramelizes, 20–25 minutes.

Transfer to a sheet of parchment and spread out in an even layer, breaking up to prevent clusters from forming. Let cool.

Do Ahead: Nuts can be candied 2 days ahead. Store airtight at room temperature.