Melt butter in a saucepan, sauté garlic for 1 minute, then whisk in flour and cook for another minute.
Slowly whisk in milk and cream. Stir until thickened, about 3–4 minutes.
Lower heat. Stir in cheese until melted, then add bacon, ranch, green onions, salt, pepper, and parsley.
Mix in shredded chicken until well coated and heated through.
Spoon filling into tortillas, fold sides, and roll up tightly.
Toast seam-side down in a skillet over medium heat, 2–3 minutes per side.
Slice wraps in half and serve warm with extra ranch if desired.