Preheat the broiler and line a baking sheet or lightly oil it.
Pat the salmon fillets dry. Rub each fillet with the olive oil, then evenly coat with 2–3 tablespoons spicy curry powder and season with kosher salt and black pepper. Drizzle honey over the top of the fillets.
Broil the salmon on the top rack until the tops begin to crisp and the fillets are mostly cooked, about 3–5 minutes; watch closely to avoid burning.
While the salmon broils, heat a large skillet over medium heat and melt 1 tablespoon of the butter. Add the red curry paste and grated ginger and cook, stirring, until very fragrant, about 2–3 minutes.
Add the chopped broccoli, coconut milk, tamari (or soy sauce), and fish sauce to the skillet. Stir to combine and bring to a gentle simmer.
Slide the broiled salmon into the simmering sauce, spooning some sauce over the fillets. Simmer gently for 3–5 minutes, or until the salmon is cooked to your liking and the broccoli is tender-crisp.
Meanwhile, in a small skillet over medium heat, melt the remaining 5 tablespoons butter with the chopped garlic and a pinch of chili flakes. Cook until the butter turns lightly brown and the garlic crisps slightly, about 2–4 minutes; remove from heat.
Serve the salmon and coconut curry sauce over bowls of rice. Drizzle the garlic-browned butter over the salmon and garnish with basil or cilantro if desired.