Bring a large pot of salted water to a boil and cook linguine according to package instructions until just al dente (usually 8–10 minutes). Reserve 1 cup pasta water, then drain.

Pat steak cubes very dry with paper towels; season with 1 tsp salt, 1/2 tsp black pepper, and smoked paprika. Toss with 1 tbsp olive oil.

Heat a large heavy skillet over medium-high heat and add 1 tbsp butter. When shimmering, add half the steak in a single layer. Sear 2–3 minutes without moving, then flip and sear another 1–2 minutes for medium-rare (adjust time for desired doneness). Remove to a plate and repeat with remaining steak, adding another 1 tbsp butter if needed. Set steak aside and loosely tent with foil.

Reduce heat to medium. In the same skillet, add remaining 1 tbsp olive oil and the extra 1 tbsp butter. Add shallot (if using) and sauté 1–2 minutes until softened. Add minced garlic and cook 30–45 seconds until fragrant — don’t let it burn.

Pour in the broth and scrape up brown bits from the pan; simmer 2 minutes to reduce slightly.

Stir in heavy cream and bring to a gentle simmer. Simmer 5–7 minutes, stirring occasionally, until sauce starts to thicken.

Lower heat and whisk in Parmesan, mozzarella, and Romano slowly until smooth. Add Dijon and lemon juice/zest, then season to taste with remaining salt and pepper. If sauce becomes too thick, thin with reserved pasta water a splash at a time. Simmer 2–3 minutes until velvety.

Toss linguine into the cheese sauce using tongs so every strand is coated, adding up to 1/2 cup reserved pasta water if needed to loosen. Warm together 1–2 minutes.

Gently fold in steak bites to reheat (or plate pasta and top with steak). Garnish with parsley and crushed red pepper flakes if you like heat. Serve immediately with extra Parmesan.