Preheat the grill to medium-high heat (about 400°F).
In a small bowl, combine garlic powder, smoked paprika, salt, and black pepper.
Pat the chicken breasts dry with paper towels. Rub 1 tablespoon of olive oil over the chicken breasts, then evenly sprinkle the spice mixture on both sides of each breast.
In a mixing bowl, toss the halved baby potatoes with the remaining 1 tablespoon olive oil, dried thyme, salt, and black pepper.
Spread the potatoes on a baking sheet in a single layer. Roast in a preheated oven at 425°F for 20-25 minutes, turning halfway through, until golden and tender.
Place the chicken breasts on the grill and cook for 6-7 minutes per side, or until the internal temperature reaches 165°F and the chicken is cooked through. Remove from the grill and let rest for 5 minutes.
While the chicken rests, prepare the salad. In a large bowl, combine mixed salad greens, sliced cucumber, cherry tomatoes, and red onion.
In a small bowl, whisk together balsamic vinegar, lemon juice, Dijon mustard, salt, and black pepper to make the dressing.
Drizzle the dressing over the salad and toss gently to combine.
Serve each grilled chicken breast with a portion of roasted baby potatoes and a generous helping of the mixed green salad.