Combine pumpkin (not pumpkin pie filling), light brown sugar, 1/3 cup granulated sugar (save 3 tablespoons of sugar), and lemon juice in a medium-sized saucepan.
Simmer uncovered for 25-30 minutes over low-medium heat. Stir constantly to prevent sticking. Mixture will turn a beautiful brownish color and will thicken.
When mixture sticks to spoon, turn heat off. Stir in vanilla, cinnamon (optional), pumpkin pie spice (or allspice), and salt.
Taste a "cooled" sample. If you prefer sweeter, stir in one teaspoon of sugar. Taste again. Repeat until satisfied with sweetness.
When satisfied with taste, simmer 10 minutes.
Cool completely before serving immediately.
Store in a lidded container. Keep refrigerated.