Place peeled, cubed potatoes in a large pot, cover with cold water, and season generously with salt. Bring to a boil, then simmer 15–20 minutes until fork-tender.

Warm the milk gently (stovetop or microwave) so it’s not cold when added to the potatoes.

Drain potatoes well and return to the hot pot to steam off excess moisture. Mash with 2 Tbsp butter, then add warm milk a little at a time until smooth and creamy. Fold in yogurt or sour cream if using. Season with salt and pepper to taste; cover to keep warm.

While potatoes cook, pat steak cubes very dry with paper towels. Season generously with salt and pepper.

Heat a large skillet over medium-high heat. Add oil and 2 Tbsp butter; when hot and shimmering, add steak in a single layer (work in batches). Sear 2–3 minutes per side until browned on the edges but still tender inside. Transfer to a plate and tent loosely with foil.

Reduce heat to medium. Add remaining 2 Tbsp butter to the skillet. Stir in minced garlic (and thyme if using) and cook 30–60 seconds until fragrant without browning.

Return steak (and any juices) to the pan. Toss to coat in the garlic butter and warm through 1 minute. Taste and adjust salt and pepper.

To serve, spoon creamy mashed potatoes into bowls or plates. Top with steak bites and drizzle all remaining garlic butter from the pan over the potatoes. Garnish with parsley if desired.