Place the greens and the broth in a large pot; add enough water to cover the greens. Bring to a boil over high heat, then reduce the heat to medium or medium-low so the liquid is barely bubbling. Cook the greens until very tender, about 40 minutes. Remove from the heat.
While the greens are cooking, make a roux: Heat the oil in a heavy pot over medium heat. Once the oil shimmers, whisk in the flour until smooth. Reduce the heat to medium-low; cook, stirring constantly, until the mixture turns a light brown color, 10 to 20 minutes.
Stir in the onion, green and red bell peppers, celery, garlic, cayenne pepper, smoked paprika, salt and pepper. Cover, and cook, stirring occasionally, until the vegetables are very tender, about 20 minutes.
Drain the cooked greens, reserving the liquid. Transfer the greens to the pot of vegetables. Measure the reserved cooking liquid and add 8 cups of it to the pot. Increase the heat to bring it to a boil, then reduce the heat until the liquid is barely bubbling. Cook for 10 minutes, just to incorporate all the flavors. Taste, and add salt and pepper as needed.
Divide the rice among serving bowls, and ladle a cup of hot gumbo over each portion. Garnish with the scallions.