Whisk together first 6 ingredients. Cook in a lightly greased large skillet over medium heat, without stirring, until eggs begin to set on bottom. Draw a spatula across bottom of skillet to form large curds. Continue cooking until eggs are thickened but still moist. (Do not stir constantly.) Remove egg mixture from skillet, and set aside. Wipe skillet clean.
Stir together Ranch dressing and salsa; set aside.
Sprinkle 1/4 cup cheese evenly onto half of each tortilla; top evenly with one-fourth of egg mixture, bacon, and ham. Top each half with 1/4 cup additional cheese. Fold tortilla in half over filling, pressing gently to seal.
Heat skillet coated with cooking spray over medium-high heat. Add quesadillas, in 2 batches, and cook 3 to 4 minutes on each side or until golden brown. Serve with salsa mixture.