Bake the prosciutto: Preheat your oven to 400°F. Lay the prosciutto slices in a single layer on a parchment-lined baking sheet. Bake for 8–12 minutes, or until crisp. Let cool, then break into small pieces.
Toast the sourdough: Arrange the sourdough slices on a baking sheet and lightly brush with olive oil. Bake at 400°F for 5–8 minutes, flipping halfway through, until toasted and golden around the edges.
Make the dipping oil: In a shallow serving bowl, combine the olive oil, balsamic vinegar, grated Parmesan, grated garlic, chopped basil, Italian seasoning, capers, and red pepper flakes. Stir gently to distribute everything evenly.
Finish the dish: Sprinkle with flaky sea salt and top with the crispy prosciutto pieces. Add a little extra Parmesan and fresh basil if desired.
Serve: Serve immediately with toasted sourdough bread for dipping.