Rinse rice until water runs clear. Drain and set aside.
In a medium pot or Dutch oven, toast the coconut and sesame seeds over medium-low heat, stirring occasionally, until fragrant, 3 to 5 minutes. (Adjust heat as needed to prevent burning.) Transfer to a small bowl. Wipe out the pot.
In the same pot, melt the coconut oil over medium-low. Add the scallion whites, turmeric, garlic, ginger, 1/2 teaspoon salt and 1/4 teaspoon black pepper and cook, stirring, until aromatic and lightly toasted, 3 to 5 minutes.
Add the rice, coconut milk, and 1/2 tsp salt. Fill the empty can of coconut milk with water (or broth) and add it to the pot. Give the mixture a good stir to separate any lumps and bring to a boil over medium-high heat.
Once boiling, cover, turn the heat to low, and simmer for 10 minutes.
As rice cooks, remove and discard any tough stems of the leafy greens, if needed. When the rice has cooked for 10 minutes, arrange the greens on top of the rice in an even layer and season well with 1 teaspoon salt and 1/2 teaspoon pepper. Cover and cook until the rice is tender, 5 more minutes. Remove from heat and let sit, covered, 5 minutes.
As rice rests, zest the lime and cut it into 4 wedges. Add zest to the coconut-sesame mixture, along with the scallion greens. Season with a pinch of salt and pepper and stir to combine.
Gently stir the greens into the rice using a spatula or fork, season to taste with salt and pepper. Divide among bowls. Sprinkle the crunch mixture on top and serve with a lime wedge.