Heat the Oil: Pour about 1 1/2 inches of vegetable oil into a deep sided pot. Heat the oil until it reaches 350F. Keep the burner temperature fairly low since you don't want the oil to heat up too fast.
Make the Fritter Batter: Whisk together the chickpea flour, rice flour, baking soda, kosher salt, and paprika.
Add the shallots, parsley, shrimp OR chickpeas, and water. Mix with a large spoon or silicone spatula until just combined. Let the batter rest for 10 minutes.
Fry the Fritters: Drop the fritters into the batter in heaping tablespoons. Fry for 5-6 minutes, or until golden brown. Don't overcrowd; fry up the fritters in 2-3 batches. When each batch is done, remove it to a towel lined platter to drain.