Pat the chicken thighs and steak dry with paper towels and season both generously on all sides with 1 tsp kosher salt, 1/4 tsp black pepper, and 1/2 tsp smoked paprika. Dry meat sears better; seasoning early begins flavor penetration.

Warm a large heavy skillet (cast‑iron preferred) over medium‑high heat and add 1 tbsp olive oil. When shimmering, sear the chicken thighs skinless side first in a single layer (you may need to do this in two batches) for 3–4 minutes per side until deeply browned — this Maillard crust adds savory, caramelized flavor and locks juices. Transfer to a plate; they will finish cooking later.

In the same skillet, add the steak and sear for 1.5–2 minutes per side for medium‑rare (longer if you prefer medium). Rest the steak on a cutting board for 8–10 minutes, then thinly slice against the grain. Quick, high‑heat searing gives the beef a flavorful crust while keeping the interior tender.

Wipe the skillet if there is an excessive burnt fond, leaving the browned bits. Reduce heat to medium and add 1 tbsp olive oil plus 1 tbsp butter. Add the diced onion and bell pepper; sauté 4–5 minutes until softened and translucent. Sweating these aromatics releases sugars and builds the base flavor for the rice.

Add the minced garlic, cumin, chili powder and remaining smoked paprika; cook 30–45 seconds until fragrant. Toasting the spices in fat 'blooms' their aroma and deepens their flavor—don’t skip this step.

Stir in the dry rice and toast it 1–2 minutes, stirring constantly so each grain is glossy with butter—this toasting gives the rice a nuttier flavor and helps keep the grains separate.

Pour in the chicken broth, diced tomatoes (with juices), corn, remaining salt and pepper. Nestle the seared chicken thighs into the rice (cut side up if bone‑in; these are boneless so just lay them gently on top). Bring to a brisk simmer, then reduce heat to low, cover tightly and cook 16–18 minutes until rice is tender and liquid absorbed. Cooking the rice with the meat on top lets the chicken finish evenly while the rice steams, integrating flavors.

Remove skillet from heat and let it rest, covered, 5 minutes. Resting lets residual steam finish the rice and the juices re‑absorb so the dish isn't watery when finished.

Uncover, remove chicken thighs to a cutting board and slice if desired. Stir 4 tbsp cold butter and the shredded cheddar into the rice until fully melted and glossy—adding cold butter finishes the rice with a silky texture and melts the cheese evenly without clumping.

Return sliced chicken and the sliced steak to the skillet, tucking them into the cheesy rice. Squeeze the juice of one lime over the whole pan and scatter chopped cilantro. The acidity of lime brightens the rich, buttery rice and balances the dish.

Taste and adjust seasoning (salt, pepper, lime). Serve hot with optional dollops of sour cream or crema and extra chopped cilantro. The contrast of cool crema against warm, cheesy rice enhances mouthfeel and flavor contrast.