In a bowl, toss the chicken with 1 tsp. curry powder and the salt and pepper.
In a large skillet, heat 1 tbsp. oil over medium-high. Add the chicken and cook until browned, 3 to 4 minutes. Transfer to a plate.
In the same skillet, heat the remaining 1 tbsp. oil over medium-high. Add the onion and cook until just soft, 2 to 3 minutes. Add the garlic and cook 30 seconds. Stir in the sweet potatoes and cook 3 minutes. Add the remaining 5 tsp. curry powder and cook, stirring, 30 seconds. Add the coconut milk and brown sugar, bring to a boil, then reduce the heat to medium.
Simmer until the sweet potatoes are tender, 7 to 8 minutes. Stir in the peas and cook 2 minutes. Stir in the chicken and cook until heated through, 1 to 2 minutes. Remove from the heat and stir in the basil.