For the shrimp: Preheat the oven to 400℉ and spray a baking sheet with olive oil or line it with parchment paper.
Rinse the shrimp and pat dry with paper towels. (Helpful hint: The coating step will be easier if there is very little moisture on the shrimp.)
Mix the cornstarch, salt, and cayenne pepper in a shallow bowl—or mix it in a zip-top bag. Add 1½ cups of the shredded coconut to a separate shallow bowl. (I like a bowl instead of a bag for this step, but you could use a bag.) Lightly beat the eggs in a small bowl. (A smaller, deeper bowl will make it easier to fully coat the shrimp.)
Start by dredging the shrimp in the cornstarch mixture, knocking off as much of the excess as you can. Then dip in the egg to fully coat; allow the excess to drip off. Finally, roll in the coconut, making sure to thoroughly coat the shrimp.
Place the coated pieces on the prepared baking sheet and repeat with the remaining shrimp. Add the remaining ½ cup of coconut, if needed, to finish out the shrimp. (More tips: Use one hand; that way the other stays clean. I toss the shrimp in the bag with the cornstarch mixture several at a time, gently shaking to thoroughly and evenly coat. After tapping off the excess, I place them on a clean plate. When all the shrimp are coated in the cornstarch, I start dipping them in the egg, using a fork to help roll them, and then coat with the coconut.)
Make ahead tip: At this point, the shrimp can be refrigerated, uncovered, for up to 2 hours.
When ready to bake, spray the top of the shrimp with the olive or avocado oil. Bake the shrimp until they are pinkish on the outside, the coconut is golden in places, and the meat is no longer transparent in the center, about 15 minutes. Flip the shrimp about ⅔ of the way through if the bottoms are nicely golden. Otherwise, there’s no need to flip. (Darker baking sheets will brown the shrimp more quickly. Jumbo shrimp may take up to 20 minutes.) In my oven, when using a dark sheet, I flip after 10-11 minutes, by which time the shrimp are lightly golden on the bottom, and then flip and cook for 4-5 minutes more. If you’re not sure, cut into one and remove from the oven as soon as the shrimp are opaque throughout. For best texture, take care not to overcook.
Serve immediately with the dipping sauce or another sauce of choice.** When serving as an appetizer, note that the shrimp will still taste good at room temperature. If taking them somewhere, I don’t cover the hot shrimp as the steam can reduce the crunchiness.
For the sauce: Stir together the preserves, horseradish, Dijon, and sriracha, and serve in a small bowl along with the baked coconut shrimp. Prep-ahead tip: May prepare several days in advance and covered and refrigerated until ready to use. Sauce yield: approximately ⅔ cup. Any leftovers are delicious with chicken, pork, salmon, and ham.