Place the 3 crustless bread slices in a shallow bowl and pour 1/3 cup milk over them; set aside to soak for a few minutes until softened.
In a large bowl or the bowl of a stand mixer, combine 1 lb ground chicken, 1 lb ground beef, 1/3 cup finely diced onion, 3 Tbsp melted butter, the 2 egg yolks, 2 Tbsp chopped dill, 1/2 Tbsp salt, and 1/2 tsp black pepper.
Add the milk-soaked bread (including any remaining milk) to the meat mixture and mix on low until just combined.
In a separate medium bowl, beat the 2 egg whites on high speed until stiff peaks form, then gently fold the beaten egg whites into the meat mixture until evenly incorporated.
Set out three shallow bowls: one with cold water for moistening hands, one with the 2 beaten eggs for dredging, and one with 1 cup Italian bread crumbs.
With wet hands, shape the meat mixture into oval patties (about 20 kotleti). Dip each patty into the beaten eggs, let excess drip off, then coat evenly with breadcrumbs. Place on a cutting board while you finish forming all patties.
Heat a large heavy skillet over medium-low heat and add equal parts light olive oil and unsalted butter (about 2 Tbsp of each suggested). When the butter sizzles, add patties without crowding—about 6 at a time.
Sauté the patties about 5 minutes per side (about 10 minutes total), flipping a few times so they brown evenly. Cook until juices run clear or an internal check shows they are done.
Transfer cooked kotleti to a plate and repeat with remaining patties, adding more oil/butter to the pan as needed.
