These nuts are the perfect nosh to keep in a bowl and eat with cocktails for the holidays. Their flavor and spice sneaks up on you after a while, which is a fun surprise. Adding the rosemary halfway through cooking allows the herb to cook through without burning or turning bitter. While it may seem an unnecessary step, tossing the nuts the first 5 minutes of cooling is important because it allows the sticky maple syrup to evenly coat them, properly seasoning them all over. The task is not arduous, so don’t skip it.
Heat the oven to 350 degrees. Using a wadded-up paper towel, grease a large rimmed baking sheet with some olive oil.
In a large bowl, combine the ¼ cup olive oil, the almonds, cashews, pecans, walnuts, maple syrup, brown sugar, kosher salt, chile flakes and paprika, if using. Toss to evenly coat the nuts in the seasonings, then spread the mixture out on the prepared baking sheet. Use a silicone spatula to scrape out every last bit of seasonings, then reserve the bowl (do not wash it). Bake for 10 minutes.
Open the oven and sprinkle the nuts with the rosemary; stir to incorporate. Continue baking the nuts until they are toasted, golden brown and shiny, 10 minutes more.
Remove the baking sheet from the oven and immediately shower the nuts with a large pinch of flaky sea salt. Scrape the nuts and all syrupy seasonings back into the reserved bowl and let cool, tossing them with a silicone spatula constantly but slowly, until the syrupy seasoning has solidified into a shiny lacquer around the nuts, about 5 minutes. Transfer the nuts back to the baking sheet, spread out in a single layer, as best you can, and let cool completely.
Break up the cooled nuts and transfer them to a serving bowl. Sprinkle with another pinch of flaky salt before serving.
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