Updated on 24/09/2019 to add more depth. Thank you to my readers for getting me to do more with this; I appreciate it when people show interest in my ideas, and when they're willing to tell me that these ideas need to be worked on.
Dwarves are not born; they're made. When a dwarf wants to make a child, they collect materials and begin their project. For some it takes months, others years to get their child together. Some dwarves find themselves overcome by a desire to construct new life - a moment of flash brilliance, akin to a eureka moment. Whilst this may be directed into other constructive pursuits, the potential to make children is always there.
The materials shape the dwarf, but the exact specifics of how are unknown. A mixture of geology and physiognomy is sought to inform the parents of what is best used for their child. The most common material is clay; easy to work with and mold, good for creating a sense of character. Others may be made of soapstone or alabaster. Dwarves with a marble birth are seen in many cultures as being of higher stock, as marble cannot be reworked once carved, meaning they were made with skilled hands and a great deal of preparation.
With no bloodlines to speak of, families and clans are defined by what materials they were made from, where those materials were collected from, and who brought them into the living world. Family relations and proximity can be defined by impurities in the building materials. Whilst an adult dwarf is for all intents and purposes made of flesh, elements of their rock-form still remain in their appearance. Parents are defined by those that crafted their body and whispered the words of life to them. This means a dwarf could have only one parent, or could have half a dozen.
Each child is unique, each one perfect and flawed in its own ways. Baby dwarves look more like golems than adults; as they age they come to resemble living things more and more. During their development they are malleable, both in mind and in body. Strict parents may threaten their children with being returned to the kiln for further work.
When they are created, they are traditionally given time to set, both physically and spiritually. This is time for the earth to find them and know their presence, and for the spirit of the child to find its way into its new body. Once this time comes to an end, the parent(s) hold their child close, whisper their name to them, and give them life.
Of course, time has taken its toll and changed the ways children come into being. Midwives can be commissioned to sculpt a child on one's behalf, or to at least take a more prominent role in smoothing out features and cleaning up the model before life is given. Households may hire the same sculptor time and time again, each with their own signature style of craftsmanship. The discovery of golemancy and the making of constructs has caused cracks in dwarven culture, with some seeing them as a human would see a newly-discovered primate, whilst others see them with the same sense of looming fear as modern man sees a robot/A.I. takeover.
Industrial creation is always an option, though many would claim the children made in the same casts and forges lack the same depth of character, the same intricacies of personhood. There is little to make them unique, no caring touch of a parent, no nurturing loved one to hold their cold body close and bring them into the waking world. In some communities, bringing new dwarves into being is overseen by a committee to ensure the construction is reasonable and follows the community's values.
In rare cases, dwarves may seek to create child clones of themselves. Whilst this is possible - reports do speak of entire clone colonies made to explore new caverns and set up duplicate settlements - the process of creation does not absolutely determine the individual's personality, only their external form.
Myths speak of the dwarves being crafted into being, then being taught how to make more of their own kind. Many more tales of old speak of heroes made from polished marble, tragic heroes covered in deep crack-like scars, and the construction of sentient prosthetic limbs crafted after losing limbs in battle.