Carrot Cake French Toast

Name: Carrot Cake French Toast
Ingredients: Butter, for greasing the baking dish; 1 loaf crusty multigrain bread; 1 1/2 cups grated carrots; 1 cup finely chopped pecans; 8 large eggs; 2 cups milk; 1/2 cup heavy cream; 1/2 cup granulated sugar; 1/2 cup firmly packed brown sugar; 4 1/2 teaspoons vanilla extract; 3/4 teaspoon ground cinnamon; 1/2 cup all-purpose flour; 1 teaspoon ground cinnamon; Pinch of kosher salt; 1 stick (8 tablespoons) cold salted butter, cut into pieces; 1/2 cup chopped pecans; 4 ounces cream cheese; 3/4 cup powdered sugar; 2 tablespoons milk; 1 tablespoon lemon juice; Warm pancake syrup, for serving