As the French would say,
"Boule-cheet"
But really, the answer to the original poster's question is, It all depends.
It depends on the definition of "Executive Chef"
Executive Chef of say, 3 sattelite kitchens, a production facility and multiple F&B outlets? This is a true definition of an "Executive Chef", a Chef who manages more than one kitchen.
One way to go about it is to get as much schooling as possible, not just cooking, but HR, accounting, and biz mngmt and lay that at the Employer's desk. But honestly, do you think the employers are going to let someone with all that schooling and no track record control all that manpower and infrastructure? The future/potential earnings of over a couple a million?
Not likely
They want to see a track record. Paper certificates are only the icing on the cake, it's what you did that counts. Not what you can potentially do, what you did, and what you didn't do, tells employers more than what you can do
What you managed in the past, how you managed it, how you grew the business, what challanges you overcame, where your shortcomings are, how you address them.
You "graduate" from a small business, to a larger with more challanges, more knowledge required and gained, then on to larger ones. No intelligent employer will put someone in charge of a large operation if that person doesn't have previous experience with a similar-albeit smaller-operation.
You will need schooling for higher management, cooking is the easy part: Cook, work, read, experiment, read more, cook more, cook under pressure, cook with obstacles, cook with creativity . That's easy.
You can get night classes in HR, in accounting, and in biz mngmt--at C.C's, correspondence, what ever. You will need this, as it's impossible to learn it all first hand, but how you learn it--whether a C.C. or University degree is not important.
Hope this helps