Preheat oven to 400°F. Coat a 13 x 18-inch half sheet pan with cooking spray.
Combine soy sauce, 1 tablespoon of the oil, honey, lime juice, 1 clove of garlic, and ginger in a large bowl. Place salmon in bowl. Toss to coat. Set aside.
In a separate bowl, combine remaining 1 tablespoons of oil, remaining clove of garlic, butternut squash, Brussels sprouts, salt, pepper, and paprika. Toss to coat. Spread on baking sheet, avoiding overcrowding. Bake at 400°F for 12 minutes. Stir vegetables and push to edges of pan, creating an open center.
Place marinated salmon fillets in the open center space of pan. Pour any leftover marinade over salmon. Bake at 400° for 15 minutes. Top salmon with green onion and sesame seeds. Serve with squash and Brussels sprouts.