Start by steaming the carrots until cooked, purée them with a fork and set aside.
For the béchamel, use a medium saucepan to heat the butter over medium-low heat until melted. Add the corn starch and stir until smooth. Cook until the mixture turns light golden, about 5 minutes.
Meanwhile, heat the milk and add it to the butter mixture in three times, whisking continuously until very smooth. Bring to a boil. Cook for 5 to 10 minutes, stirring constantly, then remove from heat. Season with salt, nutmeg and pepper. Set aside to cool completely.
Preheat oven to 350ºF/ 180ºC, with rack in lower third.
Separate the yolks from the whites and beat the egg whites to a soft peak.
Add the carrot purée along with the yolks to the cooled-off béchamel.
Gently fold in the egg-white mixture just until combined.
Grease 2 ramekins (or a small soufflé dish) and pour in the mixture, gently smoothing the top.
Transfer ramekins to oven, and bake for 45 minutes, or when puffed and golden brown on top and center is set (while baking, the soufflé might pour out of the ramekins, which is normal)
After cooked, the soufflé is puffed up and fluffy, and it will generally fall after 5 or 10 minutes as risen dough does. When this happens, it´s time to serve and enjoy :)
The low FODMAP diet allows you to eat more than one serving of carrots (75 gr), so you can eat all the soufflé.