Place the dried chickpeas in a bowl or resealable container. Fill with water to completely cover the chickpeas. Cover the container and refrigerate for 24 hours. Drain and rinse the chickpeas.
In a food processor fitted with the blade attachment, combine the pistachios, soaked chickpeas, mint, parsley, onion, coriander, cumin, baking soda, garlic and 1 tablespoon olive oil. Season with salt and pepper. Pulse the food processor until the mixture starts to come together, scraping down the sides every few pulses, making sure not to overblend. (You want it to have a slightly coarse texture; you do not want it to become a smooth paste.)
Form the falafel mixture into balls about the size of a golf ball, then lightly press into discs. Place on a sheet tray.
Preheat the oven to 200 degrees F. Line a sheet pan with a wire rack.
Heat the remaining 2 tablespoons olive oil in a large nonstick pan over a medium-high heat. Saute the falafel in batches, about 3 minutes on each side to caramelize. Transfer to the sheet pan with the rack and season with salt. Repeat as needed with more olive oil and the remaining falafel. Hold the falafel in the oven until ready to serve. Serve with the Yogurt Sauce, and sprinkle everything with the pomegranate seeds and whole mint leaves.
For the yogurt sauce: Combine the yogurt, ground pistachios, tahini, cardamom, lemon juice and zest, grated garlic, salt and pepper in a small bowl and mix with a spoon or whisk until well blended. Store in the refrigerator until ready to serve.