Place an oven rack in the center of the oven. Preheat oven to 350°F.
In a small bowl, melt 4 tablespoons of butter in the microwave. Brush the melted butter onto one side of each of the bread slices. Set the bread, buttered- side- up, on a large baking sheet and bake 10 to 15 minutes, or until lightly toasted.
Place the strawberries in a bowl and sprinkle them with 2 tablespoons of the sugar. Toss and set aside.
When the bread is toasted, reduce the oven temp. to 325°F. and set a large roasting pan half-filled with hot water on the middle rack to act as a water bath. Trim the crusts off the bread and cut each slice of bread diagonally in half into triangles.
Use the remaining 1 tablespoon of butter to grease a 9x12-inch glass baking dish at least 1½-inches deep. Line the sides of the baking dish with the pieces of bread, points up. Line the bottom of the dish with more of the bread. Stand the remaining bread, points up, wedged between the bottom slices. (Don't worry if there are some spaces in between the slices or if the pieces standing up lean over a bit.)
Scatter the strawberries onto the bread and around the baking dish. Scatter half of the chocolate chips over the bread and between the slices.
In a large saucepan, heat the half-and-half and the remaining 1 cup of sugar over moderate heat, stirring to dissolve the sugar, until the mixture is hot but not boiling.
In a medium bowl, whisk the egg yolks and whole eggs to blend. Whisk in the vanilla. Remove the hot half-and-half from the heat. Whisk the hot mixture into the eggs ½ cup at a time, gradually warming up the egg mixture and not 'cooking' it. Pour the custard through a fine sieve into the baking dish. Sprinkle the remaining chocolate chips on top. Set the dish in the roasting pan in the oven and bake for 35 to 40 minutes, or until the custard is just set. Remove from the water bath and serve warm, at room temperature, or chilled.