Cut the prosciutto slices in half crosswise and arrange in a fan on 4 dinner plates, 5 half slices per plate. Stretch plastic wrap tightly around each plate and refrigerate until needed. To save space, the plates can be stacked.
Place the peaches in a bowl and season, to taste, with salt and pepper. Pour the lemon juice and water over peaches and cover.
Heat the butter over medium heat until the foam subsides and the butter has turned light brown. Add the bay leaf, thyme, vinegar, and salt and pepper, to taste. Cook for 1 minute then add peaches and baby spinach and toss to coat.
Divide evenly among the 4 plates of prosciutto and serve immediately.