So, say a full moon happened on November 15th. How many years would pass before another full moon happened on November 15th? Is this even possible to find out?

These happen in recurring cycles... you just have to find out what those are.

Lunar cycle is 28 days. Unfortunately month days are different and when you put in a leap year it throws the days off even more. Not sure there is a formula. Here is a chart you can play with.

Full Moon Calendar - When Is The Next Full Moon?

The lunar cycle is about 29.53 days, and the year is 365.25 days. Hence there are 12.3688 lunar cycles per year. To get the full moon on the same date of a given month in a subsequent year we can assume that the full moon must be within 1/2 day plus-or-minus of the first occurrence. So, the question is: how many years does it take so that the extra 0.3688 lunar cycles per year works out to a whole number of cycles, plus or minus 1/2 day? A quick estimate: 19 years should do it, with the full moon occurring about 5 hours later than on the original day. Whether that extra 5 hours throws the occurrence into the next day would have to be checked. Alternatively, after 141 years the full moon should occur at about the same time on the same date.