Combine chickpeas, onion, garlic, herbs, salt and baking powder in a food processor; process until mixture resembles a fine meal (but stop before it reaches a puree). Refrigerate mixture 15 minutes.
Heat 2-3 inches of oil in a deep saucepan or wok while falafel mixture chills. When oil reaches 375ºF (or a small piece of bread dropped in floats and sizzles), scoop batter by heaping tablespoonfuls and form into balls. Use a slotted metal spoon to gently slide falafel into the hot oil in batches of 5-6 at a time. Fry for about 4 minutes, until deep golden brown, turning a couple of times during cooking. Remove with the same slotted spoon and drain on paper towels.
Serve falafel in pita bread with sauce and desired accompaniments.