In a medium saucepan over medium heat, melt the unsalted butter. Add the minced garlic and cook for 1 minute, stirring regularly until it becomes fragrant.

Whisk the all-purpose flour into the melted butter and garlic. Continue to cook for 1 minute, stirring to form a smooth paste.

Gradually pour in the whole milk and heavy cream, whisking continuously. Cook for 3-4 minutes, stirring constantly, until the mixture thickens.

Stir in the shredded cheddar cheese until fully melted. Add the crumbled bacon, ranch dressing, chopped green onions, and season with salt, pepper, and parsley. Mix until well combined.

Add the shredded chicken to the cheesy mixture and fold gently to ensure all the chicken is thoroughly coated.

Spoon an even amount of the chicken filling into the center of each flour tortilla. Fold in the sides and roll tightly to enclose the filling.

Heat a nonstick skillet over medium heat. Place the wraps seam-side down and toast for 2-3 minutes per side, pressing gently, until golden and crisp.

Slice each wrap in half and serve warm, with additional ranch dressing available for dipping if desired.