Melt butter over medium heat. Add onion, stir, and cook until they are translucent, 2 to 3 minutes. Add garlic and cook until fragrant, another minute or so.
Stir in flour and cook for another minute or so to cook out the starchy taste. Slowly whisk in the milk and chicken broth. Continue whisking for 30 seconds to keep clumps from forming.
Cook for 5-10 minutes or until the soup has thickened to your liking. Season with salt and pepper, to taste.
Pour into a jar or another airtight container and let cool before storing in the refrigerator. Will keep for up to a week.