Heat barbacoa meat by covering bowl with paper towel and microwaving for 1-2 minutes on High. Set aside.
While meat is heating up, whisk eggs, salt and pepper in bowl. Place a skillet over medium heat; add eggs, scrambling until soft and slightly firm. Remove pan of eggs from heat and set aside.
Place 1/4 cup shredded cheese on top of each tortilla. One at a time, place tortilla with cheese on microwave-safe plate, then cook on high power for 1 minute. Remove from microwave and top each tortilla with scrambled eggs, barbacoa meat, and pico de gallo, then wrap immediately. Serve warm.