Fill a large pot with water and bring to a boil. Add the potatoes and 4 tablespoons of salt. Reduce heat and simmer for 10-15 minutes, or until potatoes are fork-tender but not falling apart. Drain and return potatoes to the pot.
Pour in the warm bone broth, cover the pot with a kitchen towel, and let steam for 10 minutes. This infuses the potatoes with the bone broth flavor.
Let the potatoes cool slightly, then cut them in half lengthwise.
Preheat oven to 400°F (200°C). Prepare two half sheet pans or one full sheet pan by drizzling with olive oil.
Sprinkle each pan with an even layer of Parmesan cheese and parsley.
Arrange the potato halves on the pans, cut-side down, in a single layer.
Brush the tops of the potatoes with additional olive oil. Season with salt and pepper.
Roast for 20-30 minutes, or until the potatoes are golden brown and reach your desired level of crispness. Keep an eye on them during the final few minutes to avoid overcooking.
Taste and adjust seasoning with additional salt if needed.
Serve immediately while hot, enjoying the fluffy texture and rich flavors of the bone broth, Parmesan, and parsley.