Sprinkle cooked ham and chopped green onions evenly down the center of each tortilla; top each with 2 Tbsp. shredded cheese. Roll up tortillas, and place, seam sides down, in a lightly greased 13- x 9-in. baking dish.
Whisk together eggs and next 3 ingredients in a large bowl. Pour mixture evenly over tortillas.
Cover and chill at least 8 hours. Remove from refrigerator, and let stand 30 minutes at room temperature before baking.
Bake, covered, at 350° for 20 minutes; uncover and bake 15 minutes. Sprinkle with remaining 3/4 cup Cheddar cheese, and bake 3 to 4 more minutes or until cheese melts. Let stand 10 minutes before serving.