Bring a large pot of generously salted water to a boil. Add the cubed potatoes and cook for 8-10 minutes until they're just fork-tender but still hold their shape — not mushy at all. Drain well and let them sit in the colander for a minute so excess steam escapes.
While the potatoes are cooking, heat the olive oil and butter together in a large skillet (at least 12 inches wide) over medium-high heat until the butter foams but doesn't brown.
Add the drained potatoes to the skillet in an even layer — don't crowd them! If your pan can't fit all the potatoes at once, work in batches. You want each piece touching the hot surface for browning.
Cook undisturbed for 2-3 minutes until you see golden-brown edges on the bottom. Gently toss or flip with a spatula and cook another 2-3 minutes until browned on all sides. The potatoes should be crispy outside but tender inside.
Sprinkle in the chopped rosemary and minced garlic, stirring constantly for about 30 seconds — you'll know it's ready when the garlic smells fragrant but not burnt (about 1 minute).
Remove the skillet from heat immediately and add the lemon juice and zest. Toss well to distribute evenly — the potatoes will absorb some of the liquid as they rest. Season with salt and pepper to taste, starting with about 1/2 tsp kosher salt.
Let the potatoes sit in the pan for 1-2 minutes before serving so the flavors meld together. Taste one and adjust seasoning if needed. Serve warm.
