In a small saucepan cook the butter, brown sugar and corn syrup over moderate heat, stirring frequently, until smooth and tawny. Pour the mixture in an even layer into a 12"x 8" baking dish. (You can use a slightly larger baking dish but adjust the cooking time.)
Tear up bread into ragged chunks or cut into cubes about 1" in size (I cut). Add all the bread on top of sugar mixture and press lightly so the bread compresses a bit. Don't squish more than about 1/4 of the air out.
In a medium bowl or giant measuring cup with a spout whisk together the eggs, milk, cream, vanilla, and salt until combined well and pour evenly over the bread. Cover the casserole with cling wrap and refrigerate a few hours or overnight.
Preheat oven to 350 F and bring bread to room temperature.
Bake casserole, uncovered, in middle of oven until puffed and edges are pale golden, 35 to 40 minutes. The simplest method to check for doneness is with a digital thermometer. The casserole is ready when the internal temperature is 160.
Serve hot French toast immediately with fresh strawberries, butter, favorite syrup or whipped cream. It looks prettiest when pieces are served upside down.