In a stainless steel pot, combine pumpkin, sugar, brown sugar, and salt; bring to a simmer. (If using fresh pumpkin, stir until it's tender, about 20 to 30 minutes.)
Continue simmering until the mixture starts to thicken, about 20 minutes. Remove from heat and transfer to a blender; blend until smooth. Return mixture to pot and heat for 10 minutes on low until it reaches desired thickness. Remove, cool, and serve.
Feeling adventurous? Try one of these variations: Apple-Cinnamon: Add 1/2 pound of peeled and diced Granny Smith apples, 3/4 cup apple juice, 1 1/2 teaspoons ground cinnamon, and 1/2 teaspoon ground ginger. Spread this on toast for a sweet treat. Cardamom-Clove: Add 1 teaspoon ground cardamom, 1/2 teaspoon ground clove, and 1/2 teaspoon ground allspice. This slightly more savory butter goes well with meats such as pork.