How does the Princess Pea get out of the dungeon in The Tale of Despereaux?

It is so tempting to give a desperately simple answer
here:  Princess Pea walks up the stairs and out of the dungeon because Roscuro, the rat,
leads her out.

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And so, here are the words that the princess
spoke to her enemy.

She said, "Roscuro, would you like some
soup? ... I promise you, " said the princess, "that if you lead us out of here, I will
get Cook to make you some soup.  And you can eat it in the banquet hall."
...

"Really?"

"Truly.  I
promise." ...

The princess bent down before [Despereaux]. 
"You are my knight," she said to him, "with a shining needle.  And I am so glad you
found me.  Let's go upstairs.  Let's eat some soup."

And,
reader, they did.

However,
let's look at the complexity of the
issue:

• Roscuro freely offers to lead Princess
  Pea out of the dungeon because she offers him soup.


• The
  Princess Pea offers Roscuro soup due to her "empathy" after hearing his epiphany about
  not wanting to do horrible things.  "All I wanted was some light.  That is why I brougth
  the princess here, really, just for some beauty, ... some light of my
  own."


• Roscuro only has an epiphany because he smells soup
  on Despereaux's whiskers.


• Despereaux's whiskers have the
  smell of soup because Cook offers Despereaux soup before he embarks on his
  quest.


• Cook offers Despereaux soup, usually against her
  better judgement, because she has her own epiphany that soup needs to comfort another in
  order to be truly enjoyed.  "Soup needs another mouth to taste it.  Another mouth to be
  warmed by it."


• Cook only has her ephiphany because she is
  illegally cooking soup at midnight to comfort herself because the princess has been
  kidnapped.


• The Princess Pea has been kidnapped because of
  Roscuro's revenge.


• Roscuro wants revenge on the Princess
  Pea because of her look of contempt after Roscuro mistakenly falls in the Queens soup
  and kills her (through a heart attack).


• Roscuro only
  falls in the soup because he is getting a birds-eye view of the
  party.


• Roscuro only wants a birds-eye view of the party
  because he has fallen in love with light, ... the same kind of light that Despereaux
  loves as well.

So, in the words of Miggery Sow,
I must say, "Gor!" that's a long list!  Ha!  Therefore, in summary, I must say that the
Princess Pea gets out of the dungeon due to a masterful web of plot points delicately,
intricately, and exquisitely created by dear Kate DiCamillo.