Heat oven to 425°F. Line a large sheet pan and lightly oil it.
Boil potatoes in well-salted water until fork-tender, 15–18 minutes.
Drain and let potatoes steam-dry in the pot for 2–3 minutes.
Melt butter in a small saucepan. Stir in honey, garlic, smoked paprika, 1 tsp salt, and pepper.
Spread potatoes on the sheet pan. Gently smash each to about 1/2-inch thick.
Brush potatoes with olive oil, then spoon on half the honey-butter mixture.
Roast 15 minutes. Carefully flip and lightly re-smash any that puffed back up.
Brush with remaining honey-butter and sprinkle red pepper flakes if using. Roast 10–12 minutes more until crisp and caramelized. Broil 1–2 minutes if you want extra color.
Finish with parsley and a pinch more salt if needed. Serve hot.