Preheat the oven to 250 degrees F. Combine the raspberries, sugar and 3 tablespoons water in a small saucepan over medium-high heat; cook until the raspberries are broken down and the mixture is syrupy, about 5 minutes. Strain through a fine-mesh sieve into a bowl, pressing the berries with a rubber spatula.
Whisk the chocolate-hazelnut spread and eggs in a medium bowl until smooth, then transfer to a large baking dish and whisk in the milk. Working in batches, add the bread and soak, turning once, 1 to 2 minutes. (Remove before the bread is soggy.)
Melt 1/2 tablespoon butter in a large nonstick skillet over medium heat. Add 2 pieces bread and cook until browned, 3 to 4 minutes per side. Transfer to a baking sheet and keep warm in the oven; repeat with the remaining bread, adding 1/2 tablespoon more butter to the skillet with each batch. Top with the raspberry sauce and hazelnuts.