Preheat a grill to medium high. Toss the nectarine wedges with olive oil, cumin, cinnamon, cayenne pepper, and salt.
Grill the nectarine wedges until marked, 2 to 3 minutes per side. Chop and toss with the rice, lemon juice, almonds, and dill.
Toss well to combine. Add more cinnamon, cumin, cayenne, or salt if needed. Serve at room temperature or warm.