Place the cubed sweet potatoes in a microwave-safe bowl with 2 tablespoons of water. Cover and microwave on high for 4 minutes to slightly soften; drain and set aside. This speeds the skillet browning later.
Pat the steak dry with paper towels. Sprinkle both sides evenly with the kosher salt, black pepper and smoked paprika. Let sit at room temperature for about 10–15 minutes while you prep the vegetables.
Heat a large heavy skillet (cast iron works best) over medium-high until hot. Add 1 tablespoon olive oil and swirl to coat. Sear the steak 3–4 minutes per side for medium-rare (longer if you prefer well done). Transfer steak to a cutting board and tent loosely with foil; rest 6 minutes.
Reduce heat to medium and add the remaining 1 tablespoon olive oil and the butter to the now-empty skillet. Add the sliced onion and bell pepper and cook, stirring occasionally, until softened and starting to brown, about 6 minutes.
Stir in the minced garlic and cooked sweet potato cubes. Press the potatoes down into the pan and let them brown undisturbed for 2–3 minutes, then toss and repeat so they pick up a deep, caramelized color — about 8–10 minutes total. If the pan gets too dry, splash 1–2 tablespoons water to loosen browned bits.
Slice the rested steak thinly against the grain. Return the slices to the skillet and gently toss everything together just to warm the steak through, 1–2 minutes. Taste and adjust seasoning with a pinch more salt or pepper if needed.
Finish the skillet with a final small pat of butter if desired and serve hot straight from the pan.