Over high heat, bring water to a boil with the cinnamon sticks, cloves, and salt. Remove from heat and cover. Steep for about 45 minutes to 1 hour.
Remove cinnamon sticks and cloves and discard. Place rice, ½ cup pumpkin puree, honey, milk, ground cloves, ground nutmeg, and turn to high heat. Bring to a boil.
Once boiling, turn to low and cover. Let simmer for 30 to 35 minutes. Add an additional ¼ pumpkin puree and combine.
Ladle into bowls and add more milk for a thinner consistency. Serve with a dollop of whipped cream and a sprinkling of cinnamon, if desired.
