In a medium bowl, mix stuffing, melted butter, 1 egg, and cheese. Shape into balls slightly smaller than a golf ball. (If stuffing mixture is too dry to hold together, add another tablespoon of butter or a splash of chicken broth or milk.): The room fills with a warm savory scent as you fold everything together, and you will notice the mixture becoming glossier from the melted butter and egg . Work with your hands or a spoon until the components are evenly distributed, and you should feel a slightly tacky but cohesive texture that holds when pressed. This step sets the flavor balance and texture for the interior, so mix gently to avoid overcompressing the stuffing . A common pitfall is blending too slowly which leaves dry pockets, or overworking the mix so it becomes dense. If the mix crumbles and will not hold a shape, add a teaspoon of milk at a time until it comes together.
Whisk together the 2 eggs and milk in a bowl.: As you form balls, notice the way the mixture warms in your palms and compacts just enough to hold shape. Aim for uniform size so they cook evenly; they should feel firm but not packed tight. Consistent sizing ensures simultaneous browning in the oil. Avoid pressing them so hard that they become rock solid, which prevents a tender interior. If the mix sticks to your hands, lightly dampen them or oil them to make shaping easier.
In another bowl, combine bread crumbs and salt.: The whipped mixture should be smooth and slightly frothy, and it will give the bread crumbs something to cling to when you dip the balls. This egg wash adds moisture and helps the coating form a seamless crust. If the wash separates, whisk it again to re-emulsify. A frequent mistake is using a watery wash which fails to bind the crumbs, or an overly thick one that causes clumps of coating.
Dip balls in egg mixture and then coat in bread crumbs.: When you stir the crumbs and salt together, take a moment to break any lumps so the coating will be even. The seasoned crumbs should look uniform and smell faintly toasty. Mixing ahead ensures you can dredge quickly and consistently. If you wait too long to combine, crumbs can absorb moisture from the air and clump, leading to patchy coverage. Keep the bowl near your work area for speed.
Heat about 2 inches of oil in a Dutch oven to 365 degrees.: After dipping, shake off any excess egg wash so the crumbs adhere without sliding, then roll the balls in the crumbs until fully covered. You should hear a subtle rubbing sound as crumbs adhere, and the exterior will feel dry and slightly textured once coated. This double step builds the barrier that crisps in the oil and protects the center. A common error is overloading the crumbs which creates a thick, heavy crust; aim for a single even layer for the best contrast.
In batches (about 6 at a time) cook the stuffing balls until golden brown on all sides. Place on a paper towel-lined plate to absorb excess oil.: As the oil warms, you will see slight ripples and occasionally a thin wisp of steam. Maintaining a steady temperature close to 365 degrees gives you a fast sear that produces a golden shell without excessive oil absorption. Use a deep frying thermometer to monitor heat throughout, and allow the oil to return to temperature between batches. If the oil is too cool the coating will soak up grease, if too hot the exterior may char before the middle heats through. Take care when adding items to hot oil to avoid splatters.
In batches about 6 at a time cook the stuffing balls until golden brown on all sides: As they fry, listen for a steady sizzling, and watch the surface transform from pale to a deep golden tan. Turn gently with tongs so each side browns evenly and the crust forms uniformly. The internal cheese will start to soften and the aroma will intensify, signaling doneness. Overcrowding the pot drops the oil temperature and leads to uneven color and a greasy result; fry in modest batches to keep the heat consistent. Remove when evenly browned and place on a paper towel lined plate to drain, and allow a minute of rest so the interior firms slightly.