Step 1

Heat the oven to 325°F with a rack in the middle position. In a 9-by-13-inch baking dish, whisk the half-and-half, eggs, sugar, semolina and vanilla. Let stand for 10 minutes. Meanwhile, place the bread slices in a single layer on a rimmed baking sheet. Toast in the oven until the surfaces are dry and crisp but not browned, 8 to 10 minutes, flipping halfway through; they will not be dry throughout. Let cool.

Step 2

Whisk the egg mixture to recombine. Place the bread slices in a single layer in the baking dish. Let stand until most of the liquid is absorbed, 10 minutes for challah or 15 minutes for Italian bread, flipping the slices halfway through; occasionally tilt the baking dish back and forth to ensure all sides of the slices are moistened.

Step 3

In a 12-inch nonstick skillet over medium-low, melt 1 tablespoon butter until foaming. Sprinkle each of 2 bread slices with ½ teaspoon sugar, then place them sugared side down in the pan. Sprinkle the face-up side of each slice with another ½ teaspoon sugar, then cook until golden brown on the bottom, about 4 minutes. Using a spatula, flip each slice; cook until the second sides are golden brown, about 4 minutes. Transfer to individual plates.

Step 4

Wipe out the skillet. Using the remaining 1 tablespoon butter and additional sugar, cook the remaining bread slices in the same way. Serve with maple syrup.