Put potatoes, water and 1/4 teaspoon salt in a 12-inch skillet. Bring to a simmer, cover and cook over medium-low heat for 8 to 10 minutes until just tender.
Uncover and evaporate remaining water for 2 minutes. Add 1 tablespoon oil and cook potatoes over medium-high heat for 6 to 8 minutes, turning occasionally, until several faces brown; transfer to a bowl.
Pat steak cubes dry and season with remaining salt and pepper. Add remaining oil and sear steak in 2 batches for 3 to 4 minutes per batch, turning to brown several faces, until the largest pieces reach 145°F; transfer to a clean plate.
Lower the heat to low and melt butter in the skillet. Stir in garlic and rosemary for 30 to 45 seconds without browning the garlic, then add Worcestershire.
Return steak, its juices and potatoes and toss gently over low heat for 1 minute. Remove from the heat and rest for 3 minutes before dividing among 4 plates.