Step 1
Pat chicken dry, then season liberally with salt and pepper on both sides.
Step 2
Zest 1 lemon, reserving the zest for the bread crumbs, then halve the lemon and squeeze all its juice into a medium bowl. Add the eggs to the juice and beat to combine. Add the seasoned chicken and turn to coat. Let rest while you make the sauce and bread crumb mixture.
Step 3
Prepare the sauce: In a medium bowl, combine the zest and juice of the remaining 2 lemons; stir in ¼ cup of the parsley. Set aside.
Step 4
Prepare the bread crumbs: In a shallow dish, combine bread crumbs, flour, cheese, oregano and the remaining parsley. Add the reserved lemon zest and, using a fork, press the zest into the bread crumb mixture to combine evenly.
Step 5
Working one at a time, press each chicken breast into the bread crumb mixture, using your fingers to help thoroughly coat it on both sides; place on a sheet pan.
Step 6
Heat about ⅓ cup of oil in a large skillet over medium-high. Working in batches, leaving 1 to 2 inches of space between, add 2 to 3 chicken pieces and cook until golden brown, turning once, about 2 minutes per side. Transfer to a serving dish and sprinkle immediately with salt. Repeat with remaining chicken, adding and heating more oil as needed.
Step 7
While the first batch of chicken is frying, heat ⅓ cup olive oil in a small saucepan on medium heat. Add the minced garlic and cook for 1 to 2 minutes, just long enough for the garlic to sizzle but not brown. Remove from the heat and allow to cool.
Step 8
Once all the chicken is plated, slowly pour the garlic oil into the lemon and parsley mixture and whisk to combine. Before serving, spoon the salmoriglio sauce liberally over the chicken.
