Slice each chicken breast horizontally to butterfly, then cut each into two pieces so you have 4 even pieces; pat dry and season both sides with kosher salt and black pepper.
Set up three shallow bowls: one with flour mixed with garlic powder and 1/2 teaspoon salt and 1/4 teaspoon black pepper, one with beaten eggs, and one with panko mixed with 1/4 cup grated Parmesan.
Dredge each chicken piece in the seasoned flour, shaking off excess, dip into the beaten eggs, then press into the panko-Parmesan mixture until well coated on both sides; repeat for all pieces.
Heat a large cast iron skillet over medium-high and add enough oil to coat the bottom; when hot, fry 1–2 pieces of chicken at a time for about 2–3 minutes per side, or until cooked through and golden brown.
Transfer cooked chicken to a paper towel–lined plate and repeat with the remaining pieces, adding more oil as needed.
Make the lemon-yogurt dressing by whisking together the Greek yogurt, lemon juice, Dijon, honey, minced garlic, and salt and pepper to taste in a small bowl or jar until smooth; set aside.
Preheat the broiler. Slice croissants in half lengthwise, place cut-side up on a baking sheet, brush insides and tops with melted butter, and sprinkle 1/4 cup Parmesan over the tops.
Broil the croissant tops 1–2 minutes until slightly toasted and the Parmesan melts—watch closely to avoid burning—then remove from oven.
In a medium bowl, toss the chopped Romaine with the remaining Parmesan and enough dressing to coat evenly using tongs.
Assemble sandwiches by placing a breaded chicken piece on each croissant bottom (trim if needed), drizzle with hot honey if using, top with avocado slices and the dressed Romaine, then cap with the Parmesan-crusted croissant top and serve immediately.
