Combine half-and-half, sugar, and condensed milk in a large pot over medium-low heat. Bring to a gentle boil; simmer until reduced by half, about 55 minutes.
Dissolve 2 slices of bread in the half-and-half mixture; blend mixture with an immersion blender until thickened.
Preheat oven to 400 degrees F (200 degrees C).
Heat oil in a deep-fryer or large saucepan. Fry remaining bread slices in batches until golden brown, about 1 minute per side. Drain on paper towels.
Slice bread diagonally; layer slices in a 9x12-inch baking dish. Pour in enough of the half-and-half mixture to evenly soak the slices.
Bake in the preheated oven until bubbly, about 20 minutes. Flip bread slices and continue baking, about 5 minutes.