Soak the cedar planks in water for at least 30 to 60 minutes. You can soak longer if you wish. Soak until you place the salmon on top.
Preheat your grill to the highest setting.
Pat the salmon filets completely dry with a paper towel. If needed, cut the pieces so they will all fit on the cedar planks. Brush the top of the filets with mustard. In a bowl, whisk together the sugar, smoked paprika, garlic powder, salt and pepper. Sprinkle the spices on top of the mustard, covering the salmon all over. Place the salmon on the cedar planks if you haven’t already.
Toss the asparagus with the toasted sesame oil, a big sprinkle of salt and pepper and the garlic powder.
Turn the heat on the grill down to medium-high. Place the cedar planks on the grill. You want to grill the salmon with the top closed anywhere from 15 to 18 minutes, until it’s opaque and flakes with a fork.
If you have room on the grill, throw the asparagus on too when the salmon has 6 to 8 minutes left. You can use a grill basket or grill pan if it’s easier, but with asparagus I usually toss the spears right on! Grill with the top closed for 6 to 8 minutes, tossing once or twice during cook time, until charred. If you have SUPER skinny asparagus spears, you may want to cut the grill time down to 3 to 5 minutes. It just depends on the spear size!
Carefully remove the cedar planks with tongs and place them on a baking sheet to transfer inside. Place the asparagus on a plate and sprinkle with the sesame seeds. Sprinkle the salmon with chives.
Serve the salmon and asparagus immediately!