Make sauce: Combine yogurt, cucumber, mayonnaise, dill, salt, and pepper in a small bowl; mix well. Chill in the refrigerator for at least 30 minutes.

Make falafel: Mash chickpeas in a large bowl until thick and pasty; do not use a blender as the consistency will be too thin.

Place onion, parsley, and garlic in a blender; blend until smooth. Stir into mashed chickpeas until well combined.

Combine egg, cumin, coriander, salt, lemon juice, baking powder, black pepper, and cayenne in a small bowl. Stir into chickpea mixture along with olive oil. Mix in bread crumbs, a little at a time, until mixture holds together but is not sticky. Form mixture into 8 balls, then flatten into falafel patties.

Heat 1 inch oil in a large skillet over medium-high heat. Fry falafels in hot oil until brown on both sides. Serve 2 falafels in each pita half, topped with chopped tomatoes and sauce.