Heat a large skillet, preferably cast iron, over high heat. Add oil and sear corn, stirring frequently, until charred, about 3 minutes. Transfer corn to a large bowl and let cool.
Add scallions to pan and sear until charred, about 2 minutes per side. Remove from pan, chop into 2-inch pieces, and stir into the corn.
Halve avocado and remove pit and skin. Add avocado, lime juice, cilantro leaves, garlic, sugar, and salt to a blender and pulse until smooth.
Stir shaved Brussels sprouts and tomatoes into corn mixture. Drizzle in dressing and toss well. Garnish with cilantro, if desired.