Place the cucumber in a strainer, sprinkle with salt and let sit for 20 minutes. Press out the liquid.
In a large, resealable plastic bag, combine the EVOO, half the lemon juice, three-quarters of the garlic, the parsley and oregano. Season the chicken with salt and pepper, drop into the bag and marinate for 10 minutes while you preheat the broiler.
Scatter the chicken across a broiler pan and broil, turning once, until charred and cooked through, about 10-12 minutes.
Heat a griddle over medium-high heat. In a food processor, purée the drained cucumber, the yogurt, the remaining lemon juice and garlic, the mint, coriander and cumin; season with pepper.