Place the baby potatoes in a large skillet in a single layer. Add enough water to cover them, cover with a lid, and cook over medium-high heat for about 20 minutes, until fork-tender and the water has completely evaporated.
Add the olive oil and butter to the pan. Cook the potatoes for 8–10 minutes, turning occasionally, until golden brown and crispy.
Stir in the minced garlic and cook for 1 minute until fragrant. Add the paprika, smoked paprika, chili flakes, salt, and black pepper. Toss well to coat the potatoes, then finish with the chopped parsley.
In a bowl, combine the feta cheese, Greek yogurt, grated garlic, and parsley. Mix until creamy, leaving a few small feta crumbles for extra texture if desired.
Spread the creamy feta dip onto a serving plate, top with the warm garlic butter potatoes, garnish with extra parsley, and enjoy!