Preheat the oven to 375°F (190°C).
In a medium mixing bowl, combine the bread cubes. Melt the butter in a small saucepan over medium heat until it begins to brown and develop a nutty aroma. Pour the warm butter over the bread cubes and toss to coat thoroughly. Arrange the cubes in a single layer on a parchment-lined baking sheet. Bake for approximately 40 minutes, stirring occasionally, until golden brown and crisp. Toss the finished croutons with chopped parsley and set aside to cool.
Place the prosciutto slices flat on another parchment-lined baking sheet. Cover with a second sheet of parchment paper, followed by another baking tray to keep them flat. Bake for around 15 minutes until the prosciutto becomes evenly crispy. Remove from the oven, allow to cool, and set aside.
Meanwhile, prepare soft-boiled eggs by gently simmering them for about 6 to 7 minutes, then cooling them in an ice bath. Once cooled and ready to serve, peel the eggs, slice them in half, and season with a pinch of salt and pepper.
To assemble the salad, place the torn romaine into a large bowl. Add the croutons and approximately 1/4 cup of the prepared vinaigrette. Gently toss to coat the leaves evenly. Divide the salad among four plates. Top each with two egg halves, a few slices of crisp prosciutto, extra grated Parmesan, and a wedge of lemon. Serve with additional vinaigrette on the side and finish with a few cracks of black pepper.