Place baby potatoes in a large pot and cover with cold salted water. Bring to a boil over high heat, then reduce to medium and simmer for 15-20 minutes until fork-tender. Drain well and let them steam dry for 2 minutes.

Preheat your oven to 425 degrees Fahrenheit. Line a large baking sheet with parchment paper and drizzle with 1 tablespoon of olive oil.

Arrange boiled potatoes on the prepared baking sheet with space between each. Using the bottom of a glass or potato masher, gently press down on each potato to flatten it to about 1/2 inch thickness. They should crack around the edges but stay intact.

In a small bowl, mix together remaining olive oil, melted butter, minced garlic, salt, pepper, and paprika. Brush this mixture generously over each smashed potato, making sure to get into all the crispy edges.

Roast in the preheated oven for 25-30 minutes until the edges are golden brown and crispy. For extra crispiness, broil for the last 2-3 minutes, watching carefully to prevent burning.

Remove from oven and immediately sprinkle with fresh parsley and parmesan cheese if using. Serve hot with your favorite dipping sauce like sour cream, aioli, or ranch dressing.