Drain and reserve the juice from the Rotel tomatoes (about ¼ cup). Combine all sauce ingredients (chicken broth, heavy cream, honey, hot sauce, 2 teaspoons Cajun seasoning, brown sugar, mustard powder, oregano, cayenne, and red pepper flakes) in a large measuring cup and set aside.

Slice each chicken breast in half horizontally to create 4 thinner pieces total. Cover with plastic wrap and pound with a meat mallet to ½-inch thickness. Season both sides with 1 ½ teaspoons Cajun seasoning, then sprinkle 3 tablespoons flour over the surface and rub it in.

Heat 1-2 tablespoons oil in a 12-inch skillet over medium-high heat. Sear chicken for 4-5 minutes per side until a golden crust develops. Remove and set aside on a plate.

Add reserved tomato juice to the hot skillet and scrape the bottom with a silicone spatula to release browned bits. Add butter and minced garlic, cooking for 1 minute until fragrant.

Stir in 3 tablespoons flour and cook continuously for 2 minutes until the raw flour smell is gone and mixture turns slightly golden. Add the sauce mixture in small splashes while stirring continuously to prevent lumps.

Bring sauce to a boil, then reduce to a gentle simmer. Add drained tomatoes and simmer for 5-7 minutes until sauce thickens, coats the back of a spoon, and reduces by about one-third in volume.

Reduce heat to low. Slowly add shredded cheese about ¼ cup at a time while stirring continuously until melted and smooth. Stir in lime juice.

Return chicken to the skillet and spoon sauce over top. Simmer uncovered for 4 minutes. Add lime wedges and simmer 1 more minute. Remove from heat, garnish with fresh cilantro, and serve over rice.