Warm the oil in a large skillet or wide pot over medium heat. Add the onion and cook, stirring occasionally, until it becomes translucent and soft—about 4 minutes.
Stir in the garlic and ginger, letting their aromas lift for about 30 seconds. Sprinkle in the curry paste and turmeric, and cook for another minute to wake up the spices.
Toss in the sweet potato and carrot (if using). Pour in the coconut milk and broth. Bring to a gentle simmer, then reduce the heat to medium-low and cook until the sweet potatoes are just tender, about 8–10 minutes.
Gently slide the salmon chunks into the curry. Simmer for 5–7 minutes, or until the salmon is just cooked through and flakes easily. Avoid overcooking so the fish stays moist.
If you’re adding peas, stir them in during the last 2–3 minutes of cooking. Add soy sauce or tamari, salt, and pepper to taste. Finish with a squeeze of lime juice, if you like a bright finish.
Taste and adjust. If you want more heat, add a pinch of chili flakes or a splash of hot sauce. If you want it creamier, stir in a little extra coconut milk.
Garnish with chopped cilantro or parsley just before serving. Serve the curry hot with steamed rice, quinoa, or flatbread soaks up all the luscious sauce.