Cut the bread into thick slices a little shy of 1 inch (see Note). Arrange the bread in a single layer in a 13-by-9-inch pan, using an additional 8-inch square pan if necessary.
Whisk the eggs, egg yolks, and salt together in a medium bowl for 1 to 2 minutes, or until they are light, frothy, and completely smooth. (There should be no bits of egg or stringiness remaining, or you will have pieces of cooked egg on the toast.)
Whisk in the half-and-half, yogurt, granulated sugar, and 2 teaspoons nutmeg until well blended.
Pour the egg mixture over the bread. Cover with plastic wrap and refrigerate overnight, carefully turning the bread once or twice if possible.
When ready to cook, preheat an electric nonstick griddle to 350°F or heat a nonstick skillet over medium heat. Lightly brush the griddle or skillet with some butter and cook the bread in batches for 6 to 8 minutes or until golden brown on the outside but still soft in the center, turning once. Adjust the heat as necessary.
While the bread is frying, stir together the powdered sugar and 1/8 teaspoon nutmeg and put in a fine-mesh strainer.
Sprinkle the hot French toast with the powdered sugar mixture and serve topped with maple syrup or preserves.
The bread is thickly sliced so the center of each slice will stay creamy, but if the slices are too thick, the center will not cook in the time it takes to cook the outside.
