For the spicy brittle: Line a baking sheet with parchment paper.
Heat the sugar, corn syrup, butter and 1/2 cup water in a large saucepan over medium-high heat. Stir gently with a wooden spoon until the sugar has melted. Stop stirring and continue to cook, swirling the pan occasionally to ensure it cooks evenly, until the mixture reaches 300 degrees F on a candy thermometer, about 10 minutes. While this is cooking, combine the chili powder, cumin, and cayenne in a small bowl.
Carefully, but moving quickly, stir the almonds, walnuts, pecans, pistachios and spice mixture into the sugar syrup until the nuts are coated. Pour onto the prepared baking sheet, spreading it out as evenly as possible using the back of a spoon. Sprinkle over the sea salt. Allow to cool completely, 1 to 1 1/2 hours. When cool, break into shards.
For the salad: Fry the bacon in a skillet until crisp. Reserve 1 tablespoon bacon fat in the skillet.
When ready to serve, arrange the salad on a large platter in layers: escarole, radicchio, carrots, apples, onion, raisins and bacon.
Heat the skillet with the bacon fat over medium heat. Add the vinaigrette, mustard and honey and cook, stirring, until warm. Pour the dressing over the salad. Arrange the spicy brittle shards over the top. Serve immediately.