Then she took a tiny scrap of dough,
And rolled and rolled it flat;
And baked it thin as a wafer —
But she couldn’t part with that.

For she said, “My cakes that seem too small
When I eat of them myself
Are yet too large to give away.”
So she put them on the shelf.
For the third cake, the woman decided that she needn't knead a dough. Instead, she scraped out a tiny bit, possibly from her mixing bowl. Later, she rolled it as flat as she could.
She rolled and rolled it flat
By the time she put it in the oven, it was so small and thin that it seemed more like a wafer than a cake.

However, the selfish and greedy woman felt bothered. She found it difficult to part with the cake. Though it was only a tiny scrap, she was unwilling to give it way.

The selfish woman decided to keep the tiny cake for herself. She knew the cakes she had baked for Saint Peter were smaller than what she does for herself. She observes how the cakes that seemed too small when she eats them by herself were always too large to give away. So, saying this, she put it on her shelf, among her pile of cakes.
The woman even refused to part with the thin cake
Meanings of difficult words:
ScrapA small piece or amount of something, especially one that is left over after the greater part has been used
PartThe act of leaving something or someone
DoughA fairly firm mixture of flour, water, and other ingredients used for preparing bread, pastry, and biscuits
WaferA thin, light, crisp biscuit; a thin piece of something
National Council of Educational Research and Training (2006). Beehive. A Legend of the Northland - Phoebe Cary (pp. 65 - 67). Published at the Publication Division by the Secretary, National Council of Educational Research and Training, Sri Aurobindo Marg, New Delhi.