While a number of integrated amps have headphone outputs, they are typically terrible… not worth using, on even more expensive equipment.
I recommend Woo audio head amps. By and large it is all they do. If you like Audio Reseach sound this is the right brand for you. You can see my systems under my user ID.
I upgraded my headphone system to the Aurender / Ayre / Woo system I have now and it put my main system to shame. So, I had to upgrade my main system to all Audio Research Reference electronics and now they have the same character and musicality I love. I am completely happy with both. I have heard the VSi75 many times, excellent amp… if I didn’t have what I do now, I would love the VSi75… and the Woo for headphones. I own three Woo headphone amps.