Remove the fish from the fridge 15 minutes before cooking. Pat dry with paper towels and season well with salt on both sides. Set aside until ready to cook.
Mix the melted butter into the flour until combined and set aside for the sauce.
Add the eggs and milk to a shallow bowl, season with salt and pepper, and beat with a whisk or fork until well blended.
Place flour in a shallow dish and season well with salt and pepper. Mix to combine.
Dredge the fish in the flour, then the egg and back into the flour, shaking off any excess.
Set the fish aside at room temperature for 30 minutes. Frying too soon will cause the coating to fall off during cooking.
Heat oil in 12-inch skillet over medium-high heat until hot and shimmering.
Add the floured fish; cook undisturbed for 2 to 3 minutes or until golden brown. Flip and cook until golden, reaching an internal temperature of 145°F/63°C. Remove to a large platter in a single layer to keep warm.
For the Sauce
Drain the oil from the pan and wipe it clean with paper towels; if there are any scorched bits of breading in the pan, return the pan to the stove over medium heat.
Melt 2 tablespoons of the butter with the olive oil. When butter and olive oil start to sizzle, add the garlic to the pan and cook until the garlic is tender and fragrant, about 30 seconds.
Add the wine, bring to a boil and cook until almost completely evaporated, about 2 minutes.
Add the chicken stock, lemon zest, and lemon juice, and bring to a boil. Add the prepared butter and flour mixture and whisk it into the sauce until melted and combined. Cook until the sauce thickens slightly.
Reduce the heat to medium-low, add the parsley and capers, taste for seasoning, and season with salt and pepper as needed.
Serve the sauce on top of the fish garnished with lemon slices.
Notes
*For best success with this recipe, use tender to medium-firm fish fillets. Some options include cod, sole, tilapia, flounder, halibut, Branzino, sea bass, pollock, grouper, or perch.
Make sure to heat the oil thoroughly before adding the fish. Starting with hot oil is the key to a crunchy outcome.
Don't overcrowd the pan. I recommend a 12-inch frying pan. If you don't have a big enough size, cook the fish in batches. Cooking the fish too close together will result in a soggy rather than crunchy breading.
If you do not have a meat thermometer, you will know that the fish is ready when it is white and flakes easily.
To keep the fish warm as the sauce cooks, place ot on a sheet pan in an oven set to 200°F/94°C.
Serve as soon as the sauce is ready to ensure the fish stays crunchy.
Stay away from cooking wines that are loaded with salt and sugar. Instead, opt for a wine you'd enjoy drinking. Choose a dry white wine, such as Chardonnay or Pinot Grigio. Choose a wine you'd drink, not a cooking wine.
For a non-alcohol version, deglazing your skillet with stock instead of wine and skip the reduction.