Preheat oven to 425 degrees F.
Marinate the chicken. Combine the olive oil with cumin, coriander, salt, pepper, and tumeric and toss the chicken in the mixture. Let sit for 30 minutes.
Meanwhile, make the salsa verde. Blend together all of the ingredients including the olive oil, arugula, parsley, basil, lemon juice, capers, garlic, and anchovy until smooth. Season with salt and pepper and set aside.
Cut the Yukon potatoes into large chunks and place them in a medium pot. Fill the pot with enough water to submerge the potatoes and cover with a lid. Bring to a boil over high heat and continue to simmer until the potatoes are fork tender. Drain the potatoes and smash with a fork. Season with olive oil, lemon juice, grated parmesan, salt, and pepper. Set aside and keep warm.
Roast the chicken for 30 minutes or until the juices run clear.
Toss the cherry tomatoes with olive oil, balsamic vinegar, salt, and pepper. Lay the tomatoes on a sheet pan with the smashed garlic cloves. Roast the tomatoes for 15 minutes or until softened and blistered.
Portion the potatoes onto plates along with the roasted chicken and blistered tomatoes. Drizzle the salsa verde on top and serve immediately.