The verb mull means to think deeply about something, the way you might mull over your choice of what college to attend. When you mull something over, you ponder or seriously consider it.

How do you use mull over?

She woke up early in the morning and started mulling things over. We are mulling things over before finally choosing about where to live after our marriage. If I had enough time to mull things over the situation might be different. I need some more time to mull over my final decision.

Where does mull it over come from?

The grinding of a mill was the origin of mull; the metaphor was extended in America in 1873 to mental grinding; the novelist Jack London used "mull it over" in that sense in a 1910 letter.