Trim the bottoms of the asparagus. Slice the eggplant into ¾" rounds, season with salt and let rest 10 minutes before grilling. Slice shallots into thin rings and set aside in separate heat-resistant container. Cut lemon in half across its equator.
Pickle the Shallot
In a small sauce pot, combine vinegar, agave, 1 Tbsp. of water and 1 tsp. of salt. Stir over high heat until the salt is dissolved. Pour the hot liquid over the sliced shallots and set aside.
Toast Hazelnuts and Coconut
Preheat oven to 350°F. Spread hazelnuts and coconut on a foil-lined sheet tray and bake until lightly browned, 8-10 minutes. Let them cool before giving them a rough chop.
Preheat grill on high heat. Blot excess moisture from the eggplant. Drizzle the asparagus and cut side of the lemon with olive oil and season both with salt and pepper. Arrange vegetables on grill and the lemon cut side down. Flip the eggplant to brown the second side after 3-4 minutes. Roll the asparagus to char evenly. Remove lemon after cut side is charred.
Make the Arugula Salad
Drizzle the arugula with a bit of oil and season with salt and pepper.
Shingle eggplant rounds on the plate. Arrange asparagus over them and a small mound of the dressed arugula. Garnish with hazelnut-coconut mixture and the pickled shallot. One more drizzle of olive oil would do nicely.