If you are cooking indoors, heat a cast-iron ridged grill over medium heat for 10 minutes. Otherwise, start a charcoal or gas grill. In a large bowl, whisk together 1/3 cup of the olive oil, lemon juice, garlic, cumin, salt and pepper. Reserve.
In the meantime, using the remaining 1 tablespoon olive oil, and oil the chicken breasts. Cook the chicken until golden on one side, 3 to 4 minutes. Turn the chicken over, season with salt and pepper and continue to cook until done, 4 to 5 minutes (164 degrees). Slice the chicken across the grain into thin slices. Reserve.
Place the chicken stock in a saucepan and over medium high heat, reduce by three-quarters. ( The reduce stock = 1.25 cups). Add the oil/lemon juice mixture and reserve.
Bring a large pot of salted water to a boil. Add the farfalle and cook until al dente, 10 to 12 minutes. Drain the pasta and toss the pasta immediately with the oil/lemon mixture, chicken pieces, parsely, cilantro, basil, mint, arugula, preserved lemons, salt and pepper. Toss well, place on platter and serve immediately.