In a food processor, pulse chickpeas and edamame until roughly chopped. Add parsley, cumin, and 2 teaspoons salt; process until mixture is finely chopped and holds its shape when squeezed. Shape mixture into 20 balls.
Line a rimmed baking sheet with paper towels. In a medium straight-sided or cast-iron skillet, heat 1 inch oil over medium-high. Fry falafel, turning occasionally, until deep golden brown and crisp, about 10 minutes. With a slotted spoon, transfer falafel to towels; season with salt.
In a small bowl, combine sour cream, mayonnaise, coriander, and cayenne. Season with salt and serve with falafel.