Both sentences are correct, but there is a subtle difference when you add the word 'had'.
Why would someone break into my house and eat the food I made.
This is something that you are commenting on that is either currently happening, or had just finished happening. Example, you walk into your house with your friend and notice the person eating. At this point, you turn to your friend and the sentence above is what you would say.
Why would someone break into my house and eat the food I had made.
In this sentence, you are talking about something that happened a while ago. Not immediately. For example, you would use this sentence the next day.
The difference is how to express the length of time.
However, this difference is too subtle and subjective to the the perception of time. A day for one person could be eons, but a very recent even for others. So it comes down to style and preference.