How to Make It
Light a grill. Rub the chicken thighs with 2 tablespoons of the olive oil and season with salt and pepper. Arrange the chicken skin side down on the grill and top with a sheet of foil and a weighted heavy baking sheet. Grill the chicken over moderate heat until the skin is golden brown, about 5 minutes. Turn the chicken skin side up, top with the foil and weighted baking sheet and grill for 3 minutes longer. Remove the baking sheet. Turn the chicken skin side down once more and grill until the skin is crispy and the chicken is cooked through, about 2 minutes longer. Transfer the chicken to plates.
Meanwhile, in a large bowl, combine the vinegar with the shallot and garlic and gradually whisk in the remaining 1/4 cup of olive oil until well blended. Add the cucumber, onion, chile and chopped mint and season with salt and pepper. Toss to coat.
Slice the chicken; toss with the cucumber salad. Garnish with the nuts and mint leaves.