This is how garlic is stored in southern Europe. In Sicily, you will rarely pass a house without a garlic braid hanging above the front door. This protects against evil spirits!
Cooked garlic for flavoured butter? That's completely new to me. Crushed raw with a pinch of sea salt to create an oily paste, then mixed with butter (ideally with a little chilli and fresh, aromatic herbs). I also always keep a bottle of olive oil with lots of garlic cloves in it, which release their aroma into the oil. Perfect for salad dressings or simply drizzled over tomatoes or fresh baguette.