Boil the chopped potatoes in a pot of salted water until they are fork-tender, about 15 minutes. Drain well and set aside.
While the potatoes cook, season the steak cubes with salt and pepper. Heat a skillet over medium-high heat and add a tablespoon of butter.
Add the steak to the hot skillet in a single layer, letting them sear without moving for about 2-3 minutes until they develop a deep golden crust. Flip pieces and cook for another 2-3 minutes until browned and cooked to your preference.
Push the steak to one side of the skillet, then add another tablespoon of butter and the minced garlic. Sauté for about 30 seconds until fragrant, then toss the steak to coat it in the garlic butter. Keep stirring until the garlic turns lightly golden and the steak is well-coated.
Remove the cooked steak bites from the skillet and set aside. Reduce the heat to low and add a little more butter if needed. Simmer the garlic butter sauce briefly to deepen the flavor.
Return the steak to the skillet and toss to coat with the garlicky butter sauce. Keep warm as you finish the mashed potatoes.
Mash the drained potatoes with a potato masher or fork until smooth. Gradually mix in the warm milk until the mash reaches your desired creaminess. Season with salt and pepper to taste.
Spoon the warm, creamy mashed potatoes onto plates and top generously with the garlic butter steak bites. Drizzle some extra garlic butter over the top if desired for added flavor.
Serve immediately, enjoying the rich aroma and the combination of tender steak with silky mashed potatoes.