To make the creamy garlic-lime sauce, stir together all ingredients in a bowl.
Warm oil in a large skillet over medium-high heat. Add kale and a big pinch of salt and cook until wilted, about 2 minutes. Stir in the brown rice until warmed through.
Divide the brown rice between 4 bowls. Top with carnitas, avocado, tomatoes, cilantro, radishes, a lime wedge, and any other desired toppings.