Heat a large skillet over medium heat and add the olive oil. Add the sweet potato and sauté, tossing occasionally until they start to brown and turn soft. Add the mushrooms and kale and sauté a few more minutes, stirring frequently.
Turn the heat down to low and add the red curry paste and sauté an additional couple minutes. Add the coconut milk, turmeric, and ginger and stir to coat the veggies in the sauce.
Serve over rice, with a squeeze of lime juice and garnish with fresh cilantro.