In a shallow bowl, combine 3 slices of whole wheat bread with 1/3 cup of whole milk. Set aside to soak a few minutes.
In the bowl of a mixer (or you can mix by hand), combine 1 lb of ground chicken, 1 lb of lean ground beef, 1/3 cup of finely diced onion, 3 Tbsp of melted butter, 2 egg yolks, 2 Tbsp of dill, 1/2 Tbsp of salt, and 1/2 tsp of black pepper. Add the milk-soaked bread to the mixing bowl (adding any remaining milk from the plate) and mix until well combined.
In a separate medium mixing bowl, beat 2 egg whites on high speed until stiff peaks form. Use a spatula to blend the egg whites into the meat mixture until well combined.
Set up 1 bowl with some cold water to keep hands moist while forming patties. Pour 2 beaten eggs into a second shallow bowl and in a third shallow bowl, add 1 cup of dry Italian bread crumbs.
With wet hands, form patties into ovals. Dip the patties on both sides into the beaten egg, letting excess egg drip off. Finally, dip into bread crumbs and place on a cutting board until ready to sauté.
Heat a large heavy skillet over medium/low heat with 2 Tbsp of butter and 2 Tbsp of oil. When butter sizzles, add the patties about 6 at a time (don't crowd the pan). Sauté about 5 min each side (10 min total), flipping a few times while cooking. To check for doneness: juices will run clear when pierced with a knife, or simply cut one in half and take a peek inside.
