Position an oven rack about 6 inches from the broiler and preheat to 350 degrees F.
Put the crushed graham crackers in a shallow baking dish. Whisk together the eggs, egg yolks and sugar in a medium baking dish; then whisk in the milk, heavy cream and vanilla until smooth.
Put 3 or 4 slices of bread (whatever will fit comfortably in your skillet) in the custard until just soaked through, about 30 seconds per side. Let excess drip off, then dredge in the graham cracker crumbs.
Heat 2 tablespoons each of the butter and canola oil in a large nonstick saute pan over medium heat until it begins to shimmer. Cook the bread, 3 or 4 slices at a time, until golden brown and crispy on both sides, about 3 minutes per side. Place on a rack set over a baking sheet and keep warm in the oven while you cook the remaining slices.
Remove the French toast from the oven and turn on the broiler. Have 4 slices of French toast on the baking sheet and 4 on a platter. Spread each of those on the baking sheet with with 2 tablespoons of the chocolate-hazelnut spread; top with the marshmallows and broil, watching closely, until the marshmallows are bubbling and dark golden brown. Remove from the oven and top with the slices on the platter to make four sandwiches. Cut each sandwich in half diagonally and arrange two halves on each of four individual serving plates.
Heat the remaining 1/3 cup chocolate-hazelnut spread over low heat and drizzle over each sandwich. Scatter some hazelnuts on top and dust with confectioners' sugar. Serve immediately.