To effectively clean a cast iron fry pan with thick calcium deposits, start by soaking it overnight in diluted vinegar, which acts as a mild acid to help dissolve the buildup without damaging the iron. After soaking, use a wire brush or a cup-brush with a power grinder to remove the residue, or apply significant elbow grease with a metal scouring pad. Once cleaned, wash the pan thoroughly with soap and dry it completely. Next, re-season the pan by applying a thin layer of high-temperature oil, such as canola or peanut oil, and place it in the oven at a temperature just below the oil's smoke point for about an hour. After cooling, wipe out any excess oil. This process may need to be repeated after each use to achieve a durable non-stick finish. Some users also recommend heating oil on the stovetop with table salt for an additional cleaning effect, although this may be more of a traditional practice than a necessity.