1) Preheat the griddle to medium. If using hardwood or other charcoal, move it over to one side of the griddle; if using gas, leave one section off.
2) Season the chicken on both sides with salt and pepper, and drizzle well with the rapeseed oil. Place it on the griddle skin side down over direct heat, cooking until golden brown and slightly charred. Open and close the griddle, as necessary, to maintain the heat without letting the skin burn. When the skin is nicely charred and blistered, flip over the chicken and move it to indirect heat, close the lid and continue cooking until just cooked through, about 17 minutes longer, or until an instant-read thermometer inserted into the chicken registers 69C. Remove it from the griddle and let rest for 10 minutes before cutting.
3) While the chicken is cooking, brush the tomatoes, lemons and onion slices with some oil, and season with salt and pepper. Griddle the lemons cut side down until golden brown and the tomatoes cut side down until slightly charred. Griddle the onion slices, flipping once, until softened and slightly charred.
4) Make the vinaigrette by whisking the vinegar and mustard until smooth. Slowly whisk in the olive oil, then whisk in the oregano and season with salt and pepper.
To serve, carve the chicken into six to eight serving pieces and arrange it in a large shallow serving bowl. Arrange the tomatoes and onions, all but one of the lemon halves and the cucumbers over and around the chicken. Scatter the olives and feta cheese over, then drizzle with some vinaigrette. Tear the basil leaves over the dish, and then dollop the yoghurt in the centre.