Soak the liver slices in milk for 1 hour in the refrigerator, then pat completely dry with paper towels.
Season liver generously with salt, pepper, and paprika.
In a large skillet over medium-low heat, melt 2 tablespoons of butter. Add sliced onions and cook slowly for 20-25 minutes until deeply caramelized, stirring occasionally. Remove onions and set aside.
Increase heat to medium-high. Add remaining butter and avocado oil to the skillet.
Sear liver slices for 1.5-2 minutes per side until browned on the outside but still slightly pink inside (do not overcook).
Serve liver immediately topped with caramelized onions and garnished with fresh parsley.
