In a large skillet over medium-high heat, add olive oil and cook the ground turkey with garlic powder, onion powder, and smoked paprika until browned and fully cooked through (165°F internal).
Stir the black beans into the turkey mixture and cook for 2 minutes to heat through, then transfer to a bowl and set aside.
In a medium bowl, whisk together the whole eggs and liquid egg whites until well combined.
Wipe the skillet clean, return to medium-low heat, and scramble the eggs until they are just set and still moist.
Lay out the four tortillas on a flat surface.
Divide the turkey and bean mixture evenly among the center of the four tortillas.
Layer the scrambled eggs and shredded cheddar cheese over the turkey mixture.
Add 2 tablespoons of Greek yogurt and 2 tablespoons of salsa verde to each burrito.
Fold the sides of the tortillas inward and roll tightly from the bottom to seal.
Optional: Sear the burritos in a dry skillet for 1 minute per side to crisp the exterior.