How to Make It
In a blender, combine the lemon juice with the garlic, shallot, dill and mustard and puree until smooth. With the machine on, slowly pour in 6 tablespoons of the olive oil. Stir in the mint and season the vinaigrette with salt and pepper.
Light a grill or preheat a grill pan. In a shallow bowl, coat the chicken with 1/2 cup of the vinaigrette. Let stand for 5 minutes.
Meanwhile, in a large bowl, toss the yellow squash and zucchini with the remaining 2 tablespoons of olive oil and season with salt and pepper. Grill the squash and zucchini, turning once, until tender and slightly charred, about 3 minutes total. Transfer the vegetables to a platter and keep warm.
Season the chicken breasts with salt and pepper and grill over moderately high heat, turning once, until cooked through, about 10 minutes. Transfer the chicken to the platter and sprinkle with the feta cheese. Drizzle with the remaining vinaigrette and serve.