Mix softened butter, garlic, lemon juice, parsley, salt, and pepper; roll into a log using cling film and freeze for 30 minutes.
Flatten chicken breasts evenly using a mallet, being careful not to tear them.
Cut butter into chunks, place in the center of each breast, and roll tightly, securing edges.
Dredge each chicken roll in flour, dip in beaten eggs, and coat well with Panko breadcrumbs.
Chill rolled and coated chicken for 10–15 minutes to firm up.
Heat oil in a skillet over medium heat.
Fry chicken until golden brown and cooked through, about 5–6 minutes per side.
Let rest for a few minutes, garnish with parsley, and serve with lemon wedges.