Beat cream cheese at low speed with an electric mixer until creamy and smooth. Add 1 cup sugar and eggs, and beat at medium speed 2 minutes or until sugar is dissolved. Stir in 2 cups of milk, 1 cup cream of coconut, and 3 tablespoons melted butter. Stir in bread cubes. Let stand 5 minutes.
Coat a 13 x 9 inch baking dish with cooking spray. Pour bread mixture into dish. Bake at 350 degrees for 35 minutes or until set.
Stir together flaked coconut, pecans, and 3 tablespoons melted butter. Sprinkle coconut mixture over baked pudding, and bake 5 to 8 minutes more or until browned.
Stir together remaining 1/2 cup milk and 1/2 cup cream of coconut. Cook remaining 1/2 cup sugar in a medium size heavy saucepan over low heat, stirring constantly, until sugar is caramelized and mixture becomes a light brown syrup. Stir in milk mixture, and cook, stirring occasionally, 3 minutes or until sauce is thickened slightly and sugar is dissolved. Stir in remaining 2 tablespoons melted butter.
Cut bread pudding into servings and serve with caramelize sugar sauce.