Preheat the oven to 350 degrees. Brush ten cups of a standard muffin tin with softened butter. Sprinkle with the bread crumbs to coat all around, and tap out the excess.

To a large skillet over medium-high heat, add the olive oil. When the oil is hot, add the scallions and thyme. Season with 1/2 teaspoon salt. Cook and stir until scallions are wilted, about 4 minutes. Add the lettuce, cover, and cook until wilted, about 3 minutes. Uncover, increase heat to high, and cook away any excess liquid in the pan, about 1 minute. Remove from heat when the lettuce still has a little bite to it. Scrape into a bowl, and let cool.

In a large bowl, whisk together the eggs, milk, nutmeg, 1/4 cup grated cheese, and remaining 1/4 teaspoon salt. Stir in the bread cubes and the cooled lettuce mixture, and let soak 5 minutes. 

Spoon solids into the lined muffin cups to distribute evenly, then pour in the egg mixture. Sprinkle the tops with the grated cheese. Bake until golden on top and set throughout, about 20 minutes. Cool on a rack for 5 to 10 minutes, then loosen the sides with a paring knife and serve. These are good warm at room temperature.

*Use the crusts from the bread you use for cubes to make the bread crumbs to line the muffin tin. If they are very soft, dry them out in a 350-degree oven for 5 to 10 minutes.