To make the syrup: Combine 1 cup of water and brown sugar in a heavy medium saucepan. Bring to a boil over high heat, stirring until the sugar dissolves. Boil until the syrup reduces to 1 cup, about 10 minutes. Remove from the heat and whisk in the cream and cinnamon. Keep the syrup warm. (The syrup can be made 1 day ahead. Cool, then cover and refrigerate. Rewarm before serving.)
Meanwhile, prepare the French toast: Preheat the oven to 200 degrees F. Trim the bottom crust of the panettone. Starting at the bottom end of the panettone, cut it crosswise into 6 (3/4-inch thick) round slices (reserve the top piece for toast!). In a large bowl, whisk the eggs until well blended. Add the cream, milk, and sugar and whisk until well mixed. Melt 1 tablespoon of butter on a large nonstick griddle over medium heat. Dip 3 slices of panettone into the custard, turning to allow both sides to absorb the custard. Grill the soaked panettone slices until they are golden brown and firm to the touch, about 4 minutes per side. Transfer the French toast to a baking sheet and keep them warm in the oven. Repeat with the remaining butter, panettone slices, and custard.
Transfer the French toast to plates. Dollop the mascarpone atop each. Lightly dust with the powdered sugar. Drizzle the cinnamon syrup over and around the French toast and serve immediately.
Recipe courtesy of Giada De Laurentiis