Garlic Parmesan Duchess Potatoes

lbs Yukon gold potatoes (, peeled and diced into 1 1/2-inch portions)

Salt and freshly ground black pepper

butter (, divided)

garlic (, finely minced)

half and half

(slightly packed) finely shredded parmesan cheese

large egg yolks

Minced fresh parsley (, for garnish (optional))

Finely grated parmesan (, for serving (optional))