At her studio in Brooklyn on a recent morning, Na Kim sighed. She wasn’t sure about her latest painting, a portrait of a woman with brooding eyes and a sweep of dark hair.

“Because I don’t have a goal of what it should look like,” she said, “I spend time afterward thinking, ‘What do I like about it, what do I not like about it?’”

The walls and shelves were lined with dozens of variations of the portrait. Ms. Kim, a petite 38-year-old woman with a chin-length bob, had started the series about two years ago when, acting on a long-held desire to paint, she decided to finish a painting each day. Without quite meaning to, she created a vast body of work. Some of it is on view this month in “Memory Palace,” a solo exhibition at Nicola Vassell Gallery in Manhattan.

Still, she had misgivings about her latest canvas. “If it’s not sitting right with me, then it’s fine to ruin,” she said, “because it’s probably not good anyway.”

When Ms. Kim isn’t painting, she is hard at work in her vocation as the creative director at the publishing house Farrar, Straus and Giroux. Readers who do not know her name are likely to be familiar with the crisp, moody covers she has designed for scores of books including Sheila Heti’s “Pure Colour" and Michelle Zauner’s “Crying in H Mart.”