In a large pot over medium-high heat, add 2 tablespoons of the olive oil. Add the collard greens and stir-fry until wilted and tender, about 5 minutes. Season with salt and pepper and remove to a plate. Set aside.
Add the remaining olive oil along with the onions, bell pepper, and celery, and sauté until soft, about 5 minutes. Stir in the jalapeno, garlic, smoked paprika, regular paprika, cumin, cayenne, and salt. Cook for 2 minutes more, until very fragrant, then add the tomatoes, bay leaves, and thyme. Bring to a simmer and allow the tomato mixture to thicken slightly.
Pour in the stock, black-eyed peas, and brown rice. Bring to a boil, partially cover, and reduce the heat to medium-low. Simmer for 35 minutes, stirring occasionally, until the peas and rice have grown in size, but still have quite a bite to them. Cover the pot completely and continue cooking over low heat, undisturbed, until tender (but not mushy) and all of the liquid has been absorbed, another 20 minutes.
Fold in the collard greens and half the scallions. Cover and cook until the rice has absorbed all the liquid and the veggies are tender, about 10 minutes longer. Remove from the heat.
Season the vegetarian jambalaya with parsley, the remaining scallions, and serve warm.