Theory:

So she made a very little cake,
But as it baking lay,
She looked at it, and thought it seemed
Too large to give away.

Therefore she kneaded another,
And still a smaller one;
But it looked, when she turned it over, 
As large as the first had done.
Explanation:
 
Though the woman had a store of cakes on her shelf, she decided to bake a new one for him. However, it wasn't because she wanted to bake him a fresh one. Instead, the woman was quite selfish because she thought her cakes were large enough for the poor man. Of course, she didn't know it was the good Saint Peter who had stopped at her door.
 
raisin-bread-1805247_1920.jpg
The woman felt that her cakes were too large to give away

So, the woman used a small measure of dough to make the cake. However, when it started to rise in the oven, the cake became larger than she intended. So she thought it was too large to give away and decided to make another one.
 
The second time, she used a smaller size of dough to prepare the cake. She put it in the oven to bake. However, when it started to bake, she realised that the cake was as large as the first one. As a result, the woman became dissatisfied.
 
bake-49596_1920.jpg
The woman kneaded the dough to make a smaller cake
 
Meanings of difficult words:
 
S.No
Words
Meanings
1
BakeTo cook food by dry heat without direct exposure to a flame, typically in an oven
2
KneadedTo press something, especially a mixture for making bread, firmly and repeatedly with the hands and fingers
Reference:
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.