If an author is writing a story about the moment he brought hiss first child he but interrupts his story to share a childhood memory of getting a new puppy, the author is using what narrative technique?

The writing of a story within a story is known as frame story.

Explanation:

Frame story is a narrative story, where the narrator writes or tells a story within a story to fulfill the goals of his plot, more like a supporting aspect to the main story.

The author's story about his first child is the main story and sharing a memory of his childhood story is the supporting frame story. Frame story is found in various parts of literature like in art, novels, movies, opera etc,. The writing of a story within a story is known as frame story.