Combine the pumpkin, brown sugar, and salt in a small saucepan over medium-low heat; cook until the brown sugar dissolves. Remove from heat and allow to cool to room temperature.

Stir the flour into the cooled pumpkin mixture to form a dough. Add 1 teaspoon of vegetable oil to the dough; allow to rest 5 minutes. Roll the dough into 12 even-sized balls and flatten to about 2-inches in diameter.

Heat the remaining vegetable oil in a skillet over medium-hot heat. Fry the dough in the hot oil until lightly brown on each side. Drain on a plate lined with paper towels.