Use a pot big enough to hold the salmon and add enough water to cover the fish. Add the white wine and heat the mixture until vapors rise from its surface, but not to a boil. Slip the fish into the liquid and cook until done. Salmon is done when there is the first sign of a white substance forming on the surface of the fish. Remove the fish from the liquid, and let cool to room temperature; then cover and refrigerate.
To make the aioli, roast the garlic head in a 350-degree oven until soft— about 45 minutes. Squeeze the pulp from the roasted garlic into a food processor. Add mustard, egg and vinegar. With the motor running slowly, add the oil 1 drop at a time and then in a gentle stream once an emulsion has started. When the oil is used up, add the saffron infusion and season with salt and pepper. If the aioli is too thick, add more water.
Dress the greens and onion in olive oil to coat, adding a squeeze of lemon juice to taste. Season with salt and pepper. Serve the fish on top of the greens on a platter and serve the aioli on the side. .