Melt butter in a large pot.

Sauté minced onion and leeks until tender (approximately 15 minutes).

Add cubed potatoes, sliced carrots, salt, pepper, and water to the pot.

Dissolve chicken bouillon cube in 1/2 cup of boiling water and add the mixture to the pot.

Bring the soup to a boil, then reduce heat, cover, and simmer for 15 minutes.

Add uncooked rice, cover, and simmer for an additional 20 minutes.

Incorporate asparagus tips and simmer for 10 minutes. Then, add torn fresh spinach and simmer for 5 minutes, or until all vegetables are tender.

Stir in heated low-fat milk.

Season to taste.

While stirring, add heavy cream.

Heat the soup thoroughly without bringing it to a boil.

Serve immediately.