Trim the ends off the sweet potatoes, then cut each potato into 2-inch thick rounds. Place the potatoes in a large pot of water and heat over high heat until boiling. Boil the sweet potatoes until fork-tender in the center, about 20-25 minutes.
Preheat oven to 425F.
Drain the sweet potatoes, then place them on a large baking sheet that has been brushed with 1 tablespoon olive oil. Use a fork to smash the potatoes.
In a small bowl, combine the melted butter, minced garlic, and chopped parsley. Spoon the mixture onto the smashed sweet potatoes. Sprinkle salt, pepper, and the grated Parmesan cheese onto each sweet potato.
Bake at 425F for 15-18 minutes, until the potatoes are golden brown on the bottom.
Cool slightly before serving.