Heat oven to 425°F. Line a rimmed sheet pan with parchment.
Rinse potatoes, halve them, and pat very dry.
Whisk butter, olive oil, lemon zest, lemon juice, garlic, salt, and pepper.
Toss potatoes with about half of the lemon-butter mixture.
Spread on the pan, cut sides down, in a single layer.
Roast 20 minutes, then flip and brush with remaining mixture.
Roast 15–18 minutes more, until golden and tender. Sprinkle parsley and red pepper flakes.