Wash the cucumbers, slice them into thin rounds, and sprinkle kosher salt over them. Let them drain in a colander for 30 minutes.

In a skillet, heat a tablespoon of neutral oil over medium heat. Add panko breadcrumbs and toast until golden brown, about 2 minutes.

In a mixing bowl, combine chopped anchovy fillets, minced garlic, lemon juice, mayonnaise, Dijon mustard, salt, and black pepper. Gradually drizzle in neutral oil while whisking until smooth.

Pat dry the drained cucumbers and place them in a bowl. Pour the dressing over the cucumbers and toss gently.

Transfer to a serving plate, top with toasted panko breadcrumbs and shaved Parmesan cheese. Serve immediately.