In a large bowl, whisk the first 5 ingredients. In a large skillet, heat butter over medium heat. Add ham; cook and stir 1-2 minutes or until lightly browned. Pour in egg mixture; cook and stir until eggs are thickened and no liquid egg remains. Remove from heat.
Spoon a fourth of the egg mixture down center of each tortilla. Fold bottom of tortilla over filling; fold both sides to close.