In a large pot, bring 6 qt. water and 2 Tbs. salt to a boil. Add the farfalle and cook until al dente, 10 to 12 min. Drain the pasta and toss it immediately with 1 Tbs. of the olive oil. Let the pasta cool completely in the refrigerator.
Heat a cast-iron ridged grill pan or an outdoor grill. Brush the chicken breasts with 1 Tbs. of the olive oil. Grill the chicken breasts until golden on one side, 4 to 5 min. Turn the breasts, season with salt and pepper, and continue to grill until golden and cooked through, another 6 to 8 min. Let the chicken cool and then cut it on the diagonal into thin strips. Set aside.
In a large bowl, whisk the remaining 8 Tbs. olive oil with the lemon juice, garlic, and cumin. Season to taste with salt and pepper. Add the farfalle, sliced chicken, parsley, cilantro, basil, mint, and arugula and toss well. Season to taste with salt and pepper.
Put the salad into a serving bowl and serve immediately, garnished with the lemon wedges.