In a bowl, prepare the marinade by mixing together the tomato paste, brown sugar, spice blend and 2 tbsp. (1/4 cup for 4 servings) of water. Season to taste with salt and pepper. Add pork, and toss to coat in marinade. Set aside to marinate for 5 minutes.
While the pork is marinating, prepare the crema. Wash and zest the lime. Add zest to a small bowl, along with the mayonnaise, half of the lime juice and a pinch of salt. Whisk together and set aside.
Heat a large skillet over medium-high heat with a drizzle of oil. Add the marinated pork and cook for 5-10 minutes until golden brown and caramelized.
While the pork is cooking, thinly slice the romaine lettuce , and wash/dry. Drain and rinse the black beans. Thinly slice the green onions. Slice the pitas in half, then carefully open each one into a pocket. Fill the pita with shredded lettuce, carrots, black beans, green onion and barbacoa pork. Top with lime crema and any remaining lime wedges. enjoy!