In a small bowl, whisk together 2 tablespoons of olive oil with the rest of the marinade ingredients.
4 tablespoons olive oil, 1 lime, salt and pepper to taste, 4 cloves garlic, 2 teaspoons smoked paprika, 2 teaspoons cumin, ½ teaspoon Mexican oregano
Place the steak into a zip-top bag or shallow baking dish and pour the marinade over the steak. Be sure the marinade coats both sides of the meat.
2 lb sirloin steak
While the steak marinates, make the queso sauce. In a small saucepan over medium heat, melt the butter.
2 tablespoons butter
Sprinkle in the flour and whisk to combine. Allow the flour to cook 1-2 minutes, then drizzle in the milk slowly, whisking constantly.
2 tablespoons all-purpose flour, 2 cups milk
Once the mixture is smooth, add in the diced green chilies. Then, sprinkle in the shredded cheese a little bit at a time, continuing to whisk the mixture.
2 cups shredded white cheddar cheese, ½ cup diced green chilies, salt, black pepper
When the cheese is completely melted into the sauce, taste it and add salt and pepper to taste.
Turn the heat down to low and place a cooling rack over the burner. Put the pot on top of the cooling rack. This will allow the cheese sauce to stay warm without burning on the bottom while you cook the steak.
In a large non-stick or cast iron skillet over medium-high heat, add 2 tablespoons of olive oil. Once hot, place the steak into the pan. Discard the excess marinade.
Cook for 3-4 on each side or until the steak is done to your preference. Remove the meat from the skillet and set onto a cutting board to rest while you make the rice.
Use the same skillet used for the steak to make the rice. Reduce the heat to medium and melt the butter. Add the cooked rice to the pan and stir to coat. Season with salt and pepper to taste.
4 cups cooked white or brown rice, salt, 2 tablespoons butter, black pepper
Once the steak has rested for at least 5 minutes, thinly slice it against the grain. Layer your bowls with rice, steak, cheese sauce, and vegetables or other toppings.