What is the best way to cook filet mignon?

I think HalfPint has it right - I think searing on the stovetop, then finishing in the oven works best. Sounds like the oven part is maybe quicker than you've been doing - so use that thermometer and let it rest and it's pretty foolproof.

How do you like your filet? Rare, medium rare, medium, or well done? I prefer med rare, so cook the filet to 145F internal temp, then let it rest for 5 mins. Get a good reliable meat thermometer and there will be no guessing whether about how cooked your meat is, regardless of how you cook it.

You can do a hybrid of the two methods: sear on the stovetop & finish cooking in the oven. Have that meat thermometer ready and remember to let your meat rest a good 5-10 minutes before you eat it.

I heavily salt and pepper it, the sear fo3 minutes it in a super hot oiled cast iron pan, then turn it over ad put it in the over for about 6 minutes at 425 degrees. Take it out of the pan and let it rest for 5 minutes then enjoy! If you would like a pan sauce with that, after you remove the filets, put the pan back on the burner at medium heat, saute a minced shallot for minute, add 2 tablespoons of balsamic vinegar, let reduce briefy, then add 1cup of beef stock, let reduce for a couple on minutes and then swirl in a tablespoon or so of unsalted butter. Pour over filet and serve. Awesome!