Preheat the oven to 400 degrees F (200 degrees C).

Combine 3 tablespoons softened butter, brown sugar, and 1/4 teaspoon cinnamon in a small bowl; spread over 1 side each bread slice. Place bread slices, buttered-sides up, on a baking sheet.

Bake in the preheated oven until bread is crisp and topping is bubbly, 8 to 10 minutes. Cut each bread slice into 8 small triangles or squares. Set croutons aside.

Melt 2 tablespoons butter in a medium saucepan. Add onion; cook until tender. Stir in 1 can broth; bring to a boil. Cover, reduce heat, and simmer for 15 minutes.

Fill blender or the bowl of a food processor halfway with broth mixture. Cover and hold lid down with a potholder; pulse a few times before leaving on to blend. Pour into a saucepan. Repeat with remaining broth mixture.

Stir remaining 1 can broth, pumpkin purée, salt, 1/4 teaspoon cinnamon, ginger, and black pepper into puréed broth mixture; bring to a boil. Cover, reduce heat, and simmer 10 minutes, stirring occasionally.

Stir in cream and heat through; do not boil. Divide soup among serving bowls; top with croutons.