Place a kitchen towel on a baking sheet. Spread drained peas and garbanzo beans over towel and blot with another towel to dry as much as possible. Remove towels and gently place peas and beans onto light-colored or stoneware baking sheet. Drizzle with olive oil.
In a small bowl, mix brown sugar, paprika, cinnamon and salt. Sprinkle over peas and beans. Using your hands, gently but thoroughly mix oil and spices into peas and beans, and spread out in a single layer.
Roast in oven for 35 – 40 minutes, gently tossing the sheet every 10 minutes to prevent burning. Peas and beans should be crispy when done. Remove from oven, and cool slightly before serving.