Bring a large saucepan of water to a boil. Cut the potatoes in half. Add the potatoes and garlic cloves to the boiling water. Cook until the potatoes are tender, 25 to 30 minutes. Scoop out and reserve ¼ cup of the cooking water. Drain the potatoes and garlic into a colander. Transfer to a large bowl.
Mash the potatoes and garlic cloves with the olive oil, pepper and salt until combined. They won’t be completely smooth because of the potato skins. If the potatoes are a little dry, mash in some of the reserved cooking water.
Stir the prosciutto, green onions, Parmesan cheese and parsley into the mashed potatoes. Taste and season with additional salt and pepper, if necessary.
Using a spoon, place 1 ½ tablespoons of the mashed potato mixture into each muffin tin. Lightly press down the mixture.
Bake until the potato bites are browned around the edges and starting to brown on top, 25 to 30 minutes. Let rest for 5 minutes. Using a small metal spatula, remove the potato bites from the muffin tin and transfer to a serving platter. Garnish with yogurt and parsley, if desired. Serve.