Exhaust manifolds work in very punishing conditions. They conduct exhaust gasses with core temperatures that top 1,000 degrees F from the engine to the exhaust pipes. Many stock and aftermarket manifolds enhance engine performance by improving scavenging and flow dynamics of the exhaust gasses as they exit the engine head. Most manifolds are made of cast iron and cannot be welded. Any repairs involving additional metal must be done by brazing with an oxy-acetylene torch and iron brazing rods.
Clean the manifold and the broken off flange well. Be certain the parts are free of rust and carbon. Nest the flange back into position to make sure it will mate properly and be in the original plane. Clamp the broken flange with Vise-Grips at the edge furthest from the joint.
Heat the joint with a torch while holding the flange in place. Apply heat until the native metal begins to melt and puddle. Begin feeding the iron brazing rod into the puddle as the puddle begins to form. Move the torch focal point and the rod along the joint with a steady and slow motion, constantly melting the native metal and replacing it with the rod material. Braze as much as possible before stopping to flip the manifold to can gain access to the other side. Continue this process until the entire joint has been brazed.
Cool the repaired area slowly. Hold the torch back a little from the actual brazing distance and wash the flame over the repair and the surrounding area. Increase the distance of the torch gradually as the general area heats up and the repair cools, slowly pulling it back to apply less and less heat to the area while washing over a slowly-increasing area. This will slowly cool the manifold in a consistent pattern to avoid causing new stress cracks due to the thermo-dynamic expansion rate of the manifold material.
Begin removing the torch, then replace it in ever-increasing intervals once the torch has been worked back to about 18 inches from the area and the metal has lost all glow and has dropped in temperature so that the heat may be removed entirely.
File away any protruding brazing material from the mating face of the manifold. Hold the file flat and in plane with the side of the flange that did not break off. Judge the flatness of the repaired piece with the unbroken side. Remove material from the repaired flange if necessary to achieve flatness.