Boil—or better steam—the green beans in well salted water. When they are fully tender, drain them well and chop into small dice. (Or pulse in a food processor).

Sauté the minced shallot in a good pour of oil and a knob of butter just until its aroma begins to waft through the air, then add the chopped green beans. Let the green beans simmer gently for a few minutes, until they have absorbed the flavors of the shallots and butter and any excess liquid has evaporated, seasoning with salt and pepper along the way. Take off the heat and let cool completely.

Follow the usual technique (see this post for details) with the listed ingredients, using 3 Tbs of flour instead of the usual 2 Tbs. Let this cool as well.

Mix the sautéed green beans with the béchamel, along with the grated Parmesan cheese, egg yolks and  and, if using, the optional diced cheese. Season again with salt and pepper. (Go light on the salt as green beans should already be seasoned and the cheese will add savor as well.)

Pour the batter into individual ramekins that you've greased well with oil or butter, leaving some space as the batter will swell considerably during baking. Place the ramekins in a baking dish or tray and bake in a moderate (180C/350F) oven for about 30 minutes or so, until the batter is cooked through and the tops are lightly browned.

Remove the ramekins from the baking dish and let them cool, at least for a good 15-20 minutes. (Or you can let them cool completely.) The sformatini should shrink back some and detach themselves from the sides of the ramekins as they cool.

by letting the cream, with the grated Parmesan and butter, reduce in a small saucepan until it thickens enough to coat a spoon well.

on individual plates, napped with the sauce.