In a medium bowl, whisk together the milk, eggs, brown sugar, vanilla, and salt until very well blended.
Preheat on Air Fry at 375°F (190°C)for 3 minutes. Lightly oil a 7-inch(18 cm) round baking pan.
Add half the bread sticks to the egg mixture, turning to coat.
Shake the excess egg mixture off the sticks and place them in a single layer in the pan. Spray lightly with oil and cook the sticks for 4 minutes. Turn them, spray lightly with oil, and cook for 2 to 3minutes, or until golden brown.
Transfer the French toast sticks to a plate, loosely tent with foil to keep them warm, and repeat with the remaining bread sticks.
In a medium bowl, whisk the mascarpone, maple syrup, vanilla, cinnamon, and cloves until well mixed. Spoon the sauce into2 small bowls and serve with warm French toast sticks.
Refrigerate leftover sauce in a covered container for up to 5 days.