Slice potatoes 1/4 inch thick. Rinse briefly and pat very dry.
Warm a large skillet over medium heat. Add olive oil and butter; let butter foam.
Arrange potatoes in one layer. Season with salt, pepper, and paprika. Add water, cover, and cook 8 minutes.
Uncover and cook until tender and golden, 6 to 8 minutes, flipping occasionally.
Stir in minced garlic and rosemary. Cook 1 minute until fragrant.
Raise heat to medium-high. Toss to crisp edges, 2 minutes.
Off heat, add lemon juice, parsley, and Parmesan. Taste and adjust seasoning.
Notes
For extra crisp edges, microwave sliced potatoes for 3 minutes, then finish in the skillet.Swap smoked paprika for chili powder, or add a pinch of crushed red pepper for heat. Great with eggs at brunch or alongside grilled steak. Refrigerate leftovers up to 3 days; re-crisp in a hot skillet.This recipe is an original creation inspired by classic Garlic Skillet Potatoes Recipe flavors. All ingredient ratios and instructions are independently developed.