In a small bowl, whisk the eggs and egg white together until well combined.
Heat avocado oil in a large skillet over medium heat and add the ground pork.
Season the pork with smoked paprika, cumin, garlic powder, sea salt, and black pepper, breaking it into small crumbles as it browns.
Once the pork is cooked through, push it to one side of the skillet and pour the whisked eggs into the empty side.
Gently scramble the eggs until they are soft and fluffy, then fold them into the seasoned pork.
Add the black beans and fresh cilantro to the skillet, stirring for 1 minute until the beans are heated through.
Warm the whole wheat tortilla in a dry pan for 30 seconds per side until pliable.
Place the filling in the center of the tortilla, drizzle with salsa verde, fold in the sides, and roll tightly into a burrito.