Heat the oil in a large pot over medium-high until melted. Add the scallions, garlic and ginger, and season with salt. Stir occasionally until the scallions soften, about 1 ½ minutes. Stir in the turmeric and a few grinds of pepper.
Add the rice, stirring to coat for about 1 minute. Pour in the broth, coconut milk and 2 cups of water, and scrape any spices from the bottom of the pot.
Raise the heat to bring the liquid to just under a boil, with bubbles starting to break across the surface, then reduce the heat to maintain a simmer with small bubbles actively breaking across the surface. Let cook for 10 minutes, stirring occasionally to make sure nothing is sticking on the bottom.
Stir in the greens and cook until the greens and rice are tender, about 5 minutes more.
Stir in the soy sauce and most of the cilantro and squeeze in the juice of half the lime. Taste and add more lime or salt as needed.
Garnish with the remaining cilantro, a few grinds of black pepper and crushed red pepper, if using, and serve.