In a medium sized saucepan, melt butter over medium heat. When butter is melted, add flour whisking constantly till mixture turns into a paste.
Slowly add in your milk, whisking constantly to ensure there are no lumps.
Add seasonings and cook till the sauce is almost boiling and has thickened in consistency.
Add cream cheese and shredded cheddar cheese to the sauce and continue whisking till both cheeses are melted. Take off heat.
In a large bowl, combine chopped chicken and 3/4 cup of the sauce. Mix until all the chicken is coated but not too soupy.
Using a large spoon or cookie scoop, form the chicken mixture into patties. Place on a baking sheet or plate that is lined with parchment paper. Freeze for 30 minutes.
Meanwhile, prepare the breading station. Beat together eggs and 1 Tbsp. Cold water to a medium sized bowl. set aside.
Place breadcrumbs in a shallow bowl and place next to the egg mixture.
Remove the chicken patties from the freezer and dip each patty into the beaten egg mixture and coat with breadcrumbs.
Heat oil in a skillet over medium heat. Fry the patties until golden brown and heated through. About 4-5 minutes on each side.
After frying, place the patties on a plate lined with paper towels to drain excess oil.
Serve with mashed potatoes and reserved sauce.