What is the most effective way to track profit/loss per employee per month when headcount is constantly growing intramonth?

Like with every answer it all depends. Are you referring to the entire company? A subsidiary? A division? A business Unit? The point of reference would matter based on whether you are working at a global, regional or subsidiary level.
However, you can start by understanding your reporting aspect of the headcount (how a new HC or a Vacancy is reported) and differentiate between FTE and actual heads. A part-time HC is not the same a as full-time HC from a productivity measurement stand point.
Also, you might want to take a snap shot in one month and exclude new HC additions and associated costs. You will also need to adjust for vacancies. Keep in mind that HC/FTE total is usually reported as a net number.

I take the average Full Time Equivalent per month. Full-time are valued at one, Part-time at .5. Take the number on Day 1 of the month, add the number on the last day of the month, and divide by two. If applied consistently, this is good enough for comparison and analysis.

As a supplement to the methodologies already mentioned, you might want to introduce some appropriate lag factor. Whether, how, and to what extent all depend on the fact set at hand. But the point is it's rarely the case that a new head has an immediate impact on the bottom line (other than their salary, of course). Thus you might consider matching the weighted-average headcount in Month X against the bottom line of Month X + 2 (for example).

Looking at it another way, if you have a list of month headcount averages and a list of monthly net profits, just shift one of the lists up or down a bit for a better cause-and-effect matching.