In a large bowl, whisk the olive oil, lemon or lime juice, salt, garlic, shallots, cumin, cayenne, and cilantro. Add the salmon and turn to coat. Let marinate 15 minutes at room temperature.
Meanwhile, preheat a grill, burner griddle, or cast iron grill pan to medium-high.
Brush the grill with vegetable oil. Grill the salmon until marked on the bottom, about 4 minutes. Turn and continue grilling until marked on the other side and cooked through, 3 to 4 more minutes.
Divide the salmon among plates. Drizzle with more lemon juice if desired and serve with salad greens and rice.
Notes
You can also cut the salmon into portions before grilling or buy individual fillets.