Preheat a grill or griddle pan over medium heat.
In a bowl, whisk together the garlic powder, oregano, lemon juice, and olive oil to make the marinade. Season to taste with salt and pepper. Adjust the flavor until the marinade tastes balanced. Set aside half of the marinade to use for brushing the buns.
Brush one side of the butterflied chicken breast with the marinade and season with salt and pepper.
Place the brushed side of the chicken on the hot grill or pan. Brush the top side with more marinade. Cook for about 6 minutes until grill marks appear.
Flip the chicken and brush with the remaining chicken marinade. Close the grill (or cover the pan) and cook for another 6 minutes, or until the chicken reaches an internal temperature of 165°F (74°C). Remove and let rest for 5 minutes.
Brush the insides of the brioche buns with the reserved marinade. Toast or grill until golden brown and set aside.
To assemble the sandwich, spread mayonnaise on the inside of both bun halves. Layer with butter lettuce, tomato slices, the grilled chicken, Swiss cheese, and sliced red onion.
To make the mango lassi, combine the chopped frozen mango, yogurt, milk, cardamom powder, and sugar in a blender. Blend until smooth. Taste and adjust sweetness if desired.
Serve the grilled Greek chicken sandwiches with the carrot sticks, hummus, and mango lassi.