Preheat the grill or your pan to a medium heat.
Combine the spices in a bowl. Rub both sides of the salmon with the olive oil and then add the spice mix on both sides. Season with salt and pepper as desired.
Place salmon, carrots and onions on the grill or in the pan and grill for 4 minutes per side. If the salmon filets are thick you can grill them for another minute per side to ensure they're cooked all the way through. If you don't want to grill the carrots and onions just chop and dice them while the salmon cooks.
Divid the lettuce and vegetables among 4 plates. Build the plate with the bibbb/butter lettuce and arugula as a base. Layer in the vegetables and lay the salmon over the top.
Serve immediately with the dressing and the Gremolata over the salmon. You can squeeze a little more lime over the salmon and then season per taste with additional salt and pepper. Add additional fresh basil as desired.