Place all of the salsa ingredients in a medium bowl and mix to combine. Set aside.

In a medium bowl, whisk the eggs with the smoked paprika and salt. Set aside.

Heat a large nonstick pan over medium-high heat. Add the sausage and cook, stirring frequently, until browned, 4 to 5 minutes. Use a slotted spoon to transfer the sausage from the pan to a plate, leaving the drippings in the pan. Reduce the heat to low. Add the eggs and scramble until just cooked through. Transfer the eggs to a plate. Clean the pan.

Spoon about ¼ cup of the avocado-tomato salsa onto each tortilla, followed by a quarter of the sausage, a quarter of the eggs, and ⅓ cup cheese. Fold in the sides of the tortilla over the filling and roll, tucking in the edges as you go.

Lightly coat the pan with oil and set over medium heat. When the pan is hot, add the burritos, seam side down. Cook, covered, until the bottom of the burritos are golden brown, about 3 minutes. Flip the burritos over and continue cooking, covered, until golden, a few minutes more. Serve warm.