STEP-BY-STEP ANSWER:
Step 1: Recognize that the process is called oogenesis.
Step 2: Understand that oogenesis begins in the ovaries, with the formation of oogonia before birth.
Step 3: Observe that each menstrual cycle triggers the maturation of an oocyte from its arrested state.
Step 4: Note that hormonal signals, including estrogen and progesterone, regulate the maturation and release of the egg.
Final Answer: Egg cells are produced through oogenesis in the ovaries, a hormonally controlled process that involves the maturation of an oocyte during each menstrual cycle.