Position a rack in upper third of oven; preheat broiler to high. Line a baking sheet with foil and coat with cooking spray.
Whisk 2 tablespoons gochujang, 1 tablespoon mirin, 1 tablespoon tamari, 1 tablespoon honey, ½ teaspoon sesame oil, ¼ of the garlic and 2 teaspoons ginger in a small bowl. Pat 1 ¼-pound salmon dry and place skin-side down on the prepared pan. Brush the salmon with the glaze. Broil until the salmon is just cooked through, 5 to 8 minutes, depending on thickness.
Meanwhile, heat the remaining 1 teaspoon sesame oil in a large skillet over medium-low heat. Add the remaining 3 cloves garlic and cook, stirring, until fragrant and just starting to brown, about 3 minutes. Add 8 cups spinach and cook, stirring, until wilted and the pan is dry, about 3 minutes. Remove from heat and stir in the remaining 1 tablespoon tamari.
Serve the salmon over the spinach.
