Prep the potatoes: Rinse and dry thoroughly. Dry potatoes crisp better.
Start the potatoes: Heat a large heavy skillet (cast iron is ideal) over medium-high. Add 1 tablespoon olive oil.
Arrange potatoes cut-side down in a single layer. Sprinkle with 1/2 teaspoon salt. Cook undisturbed 5–6 minutes until deep golden.
Crisp and finish: Flip potatoes, reduce heat to medium, and cook another 6–8 minutes, stirring occasionally, until tender and crisp.
Transfer to a plate and tent with foil.
Season the steak: Pat steak cubes dry. Toss with 1/2 teaspoon salt, black pepper, and smoked paprika.
Sear in batches: Increase heat to medium-high. Add remaining 1 tablespoon olive oil.
Add half the steak in a single layer, without crowding. Sear 1–2 minutes per side until browned and medium-rare inside. Remove to a plate.
Repeat with remaining steak.
Make the garlic butter: Reduce heat to medium-low. Add butter to the skillet. When melted, add garlic and thyme.
Stir 30–45 seconds until fragrant; don’t let the garlic brown.
Bring it together: Return potatoes and steak (with juices) to the pan. Toss to coat in the garlic butter for 30–60 seconds. Turn off heat.
Stir in parsley and a squeeze of lemon juice if using. Taste and adjust salt.
Serve: Garnish with extra parsley. Serve with a simple green salad or steamed veggies.