• Preheat oven to 375°F. Thinly slice one-third of onion. Toss slices with ¼ cup orange juice, ¼ cup vinegar, and ½ tsp. salt in a small bowl; set aside.
• Pulse chickpeas, garlic, coriander, cumin, ¾ cup parsley, 1 tsp. salt, and remaining onion in a food processor until very coarsely chopped, about 30 seconds. Add flour and baking powder and pulse a few more times to combine.
• Lightly oil a rimmed baking sheet. Using a ¼-cup measuring cup, portion out 12 ping pong-sized balls and place on sheet, spacing 1" apart. Gently press down on tops to flatten slightly. Brush tops with 1 Tbsp. oil. Bake falafel, turning balls halfway through, until golden brown and crispy, 20–25 minutes. Wrap pitas in foil and warm in oven during last 5 minutes of baking.
• Meanwhile, whisk ¼ cup oil and remaining ¼ cup plus 1 tablespoon orange juice, 2 tsp. vinegar, and 1 tsp. salt in a medium bowl. Whisk in tahini and ¼ cup water until a smooth sauce forms.
• Whisk 2 Tbsp. pickling liquid from reserved onions with remaining 3 Tbsp. oil in another medium bowl. Add cabbage, tomatoes, and onions and toss to coat.
• Cut each pita into 4 pieces. Drizzle falafel with 2 Tbsp. tahini sauce and top with remaining ¼ cup parsley. Serve with pita, hummus, salad, and remaining tahini sauce alongside.

Do Ahead

• Falafel can be made 5 days ahead; store in an airtight container and chill, or freeze up to 1 month.