Bring a large pot of salted water to a boil over high heat. Blanch asparagus for 1 to 2 min., depending on thickness. Immediately transfer asparagus to a bowl of ice water to cool. Remove and pat dry. Refrigerate until needed.
Preheat oven to broil. Slice 2 tangerines in half crosswise. Zest the third and set zest aside. Mix cinnamon, nutmeg, cayenne and half the salt and pepper in a small bowl. Sprinkle cut sides of tangerines with spice mix and set them, spice side up, in a foil-lined roasting pan. Spoon honey overtop of each half.
Toss asparagus with oil and remaining salt and pepper and place in a single layer in the pan alongside fruit. Broil in top third of oven until honey has caramelized and asparagus is lightly blistered, about 4 to 5 min. Transfer asparagus to a platter, slice fruit into wedges and arrange alongside. Garnish with the reserved zest.
Blanch asparagus the day before or even the morning of your supper and store in the fridge until they’re ready for the broiler.