Heat a large skillet over medium-high heat and add olive oil or butter. When the fat shimmers, add the diced potatoes in a single layer and sear undisturbed for 4–5 minutes.

Stir the potatoes, season lightly with salt, and cook another 6–8 minutes until fork-tender and browned. Transfer to a plate and set aside.

In the same skillet, add the chopped onion and cook until translucent and starting to brown, about 4 minutes. Add the garlic and cook one minute more.

Add the ground beef to the onions and garlic, breaking it up with a spatula and browning until no pink remains, about 6–8 minutes. Drain excess fat if desired.

Stir in the tomato paste, thyme, smoked paprika, salt, and pepper. Cook for 1 minute, then add the beef broth, scraping up any browned bits.

Return the potatoes to the skillet and stir gently to combine. Lower the heat to medium-low and simmer for 5–7 minutes.

If using peas or carrots, stir them in now and cook until heated through.

Finish with a knob of butter or a splash of cream, sprinkle with parsley, and serve warm.