Heat the oven to 300 °F with racks in the upper and lower thirds.
Slice the challah into 1-inch cubes. Divide between two sheet pans and spread into an even layer. Bake, rotating the pans top to bottom halfway through, until dry to the touch but not browning, about 15 minutes. Let cool for 5 minutes. Increase the oven temperature to 425°F.
Meanwhile, in a blender, combine the cottage cheese, milk, eggs, maple syrup, vanilla, cinnamon, and salt. Blend until smooth.
Transfer the toasted bread cubes to your largest mixing bowl (or divide between two bowls). Pour the custard over top and use your hands to toss the bread in the custard. Let sit until most of the custard has been absorbed, 5 to 10 minutes.
While the bread soaks, generously butter one of the baking sheets with room-temperature butter. In a small bowl, combine the granulated sugar with 1 teaspoon cinnamon for the topping.
Give the bread another toss with your hands, then spread onto the baking sheet in a single layer, making sure to spread it all the way into the corners. If there are a few areas that feel sparse, don't stress: the cubes will puff and expand in the oven. Drizzle the bread with any remaining custard left in the bowl (there shouldn't be much).
Drizzle the melted butter over top, then sprinkle with the cinnamon sugar. Bake on the upper rack until the custard is set and the bread is golden and crisp in spots, 15 to 20 minutes.
Dust with powdered sugar, then top with the raspberries. Slice into 8 large rectangles, then serve with a generous amount of maple syrup.
