If using a whole pumpkin: Peel pumpkin and remove seeds. Cut flesh into ½-inch cubes. Place in medium pot with water barely to cover; bring to a boil and simmer, covered, until very soft, about 30 minutes. Drain and mash pumpkin until well pureed. If using canned pumpkin, skip and start with Step 2.
Return fresh pumpkin puree (or place canned pumpkin puree) to pot, along with remaining ingredients; stir well. Bring to a boil over medium-high heat, stirring. Reduce to a simmer and cook until thickened and cohesive, about 30 to 40 minutes, stirring and scraping bottom of pot regularly.
Allow pumpkin butter to cool to room temperature. Serve at room temperature or well chilled. Store in airtight containers in the fridge for up to 1 week.