Beat eggs and milk in large bowl. Add Smokehouse Pepper and garlic powder; mix well. Set aside.
Melt butter in large nonstick skillet on medium-high heat. Add ham and onion; cook and stir 5 minutes or until onion is softened. Add egg mixture; cook and stir 3 minutes or just until eggs are firm. Remove from heat. Add cheese; stir gently.
Spoon about 1/2 cup egg mixture into each warmed flour tortilla. Fold into burritos to serve.