Add coconut milk, cream of coconut, cloves, ½ tsp. cinnamon and salt to medium saucepan over medium-high heat. Bring to simmer, stirring occasionally. Remove pot from heat; let steep 15 minutes. Remove and discard cloves.
In medium mixing bowl, lightly beat eggs. Add coconut milk mixture ½ cup at a time, whisking vigorously after each addition to prevent eggs from cooking; set aside. In medium dish, combine shredded coconut with remaining cinnamon until evenly coated; set aside.
Melt butter on large griddle over medium heat. Working in batches, dip bread into coconut milk mixture until completely saturated. Gently transfer bread to plate with shredded coconut; flip to coat. Transfer bread to griddle. Cook, flipping once, until golden brown on both sides and warmed through, about 6 minutes per batch.
To keep your Coconut French Toast warm and fresh for up to 2 hours, simply transfer cooked toast to foil-lined baking tray. Place in oven heated to 180°F. This low oven temperature will keep the toast warm without the risk of overcooking it.