Add the Spanish rice, ⅔ cup water, and a pinch of salt to a small saucepan and bring to a boil. Cover, reduce heat to low, and cook until all of the water is absorbed and the rice is tender, about 12 to 15 minutes.
Stack the lettuce leaves and thinly slice. Roughly chop the pickled jalapeños. Zest the lime and cut half into wedges. Drain and rinse the black beans.
Add the cashew butter, nutritional yeast, ground turmeric, smoked paprika, ½ tsp salt, and ½ cup cold water to a large nonstick skillet. Whisk continuously to combine and bring sauce to a simmer. Cook until thickened, about 1 minute. Add the juice from just half the lime and as many chopped pickled jalapeños as you like. Stir, and remove from heat. Transfer the jalapeño queso to a bowl and cover to keep warm. Wipe out the skillet.
Once the rice is cooked, stir in the black beans and just ½ tsp lime zest. Warm the gluten-free wraps by wrapping them in a damp paper towel and microwaving for 30 seconds. Lay the warmed wraps on a clean work surface. Divide the sliced lettuce between the wraps and top each with ½ cup rice and beans. Carefully roll the burritos, tucking in the sides as you go.
Return the skillet to medium heat with 2 tsp vegetable oil. Once hot, add the burritos, seam side down. Cook until golden brown, about 2 to 3 minutes per side.
Cut the Black Bean & Rice Burritos in half and serve with the jalapeño queso for dipping. Serve with lime wedges and any remaining Spanish rice and beans on the side.