In a large bowl, whisk together the eggs, half-and-half (or milk), vanilla extract, cinnamon, brown sugar, and salt. Mix until everything is smooth and fully combined with no streaks of egg white left.
Use a toothpick or skewer to poke a few holes in the bottom of each roll so the custard can soak in evenly. Then dip a few rolls at a time into the egg mixture and let them soak for about 30 seconds. Avoid soaking too long, or the rolls may become soggy.
Melt about 2 tablespoons of butter in a non-stick skillet over medium-low heat. Place the soaked rolls in the pan, a few at a time, and cook until each side is golden brown. Rotate them carefully so they brown evenly without burning.
Once the rolls are golden on all sides, remove them from the pan and serve while warm. Sprinkle with powdered sugar, drizzle with maple syrup, and top with fresh fruit. For a balanced brunch, serve with bacon or sausage on the side.