Pat the chicken dry and season lightly with salt. This helps every bite stay juicy as it cooks.
In a large skillet or wide pot, heat the oil over medium-high heat. Add the chicken and sear until lightly browned on the edges, about 4-5 minutes. You don’t need to cook it through completely at this stage.
Push the chicken to the side, add the curry paste to the pan, and let it bloom for about 20-30 seconds. Stir it into the chicken to coat well and wake up the spices.
Pour in the coconut milk and chicken broth. Stir to combine. Add the sweet potatoes, onion, garlic, and ginger. Bring to a gentle simmer.
Reduce the heat to medium-low and simmer uncovered for about 15-20 minutes, or until the sweet potatoes are tender and the sauce has thickened slightly.
Stir in the fish sauce, brown sugar, and lime juice. Taste and adjust: a squeeze more lime, a pinch more sugar, or a splash more fish sauce can balance the flavors.
If you like it hotter, add a pinch of red chili flakes. For a smoother texture, you can mash a few sweet potato chunks against the back of the spoon to thicken the curry a touch.
Garnish with chopped cilantro or Thai basil before serving. Serve hot over steamed jasmine rice or with crusty bread to sop up the sauce.