The invention is a method and apparatus for iron-making / steel-making using a modified rotary hearth furnace, that is a finisher-hearth-melter (FHM) furnace. In the method the refractory surface of the hearth is coated with carbonaceous hearth conditioners and refractory compounds, where onto said hearth is charged with pre-reduced metallized iron. The pre-reduced metallized iron is leveled, then heated until molten, and then reacted with the carbon and reducing gas burner gases until any residual iron oxide is converted to iron having a low sulfur content. Nascent slag separates from the molted iron forming carburized iron nuggets. The nuggets are cooled, and then the iron nuggets and the hearth conditioners, including the refractory compounds, are discharged onto a screen, which separate the iron nuggets from the hearth conditioner. The hearth conditioner is recycled, and the iron nuggets are either prepared for sale or for additional treatment, such as alloying, in a final melter, where the final melter is preferably an electric furnace. Exhaust gases from the FHM furnace are recovered for calcining coal into fuel gases and coke.