First make the apricot-mustard glaze: Heat the butter in a small saucepan over medium heat until melted, but not browned. Add the shallot and garlic, sprinkle with salt and sweat the shallot over medium-low heat until soft and tender, 5 to 6 minutes. (Take care not to brown the shallots.)
Add the white wine and cook until most of the wine has evaporated, 2 to 3 minutes. Add the apricot jam and mustard and stir until well combined. As the jam starts to melt, continue to stir and cook for 3 to 4 minutes. Remove the sauce from the heat and set aside to cool.
Put the side of salmon, skin side down, on a large sheet of foil. Season the salmon generously with salt, and then spread half of the apricot- mustard glaze on the salmon. Set aside and reserve the extra sauce.
Preheat the grill or a grill pan on medium heat.
Put the salmon, still on the sheet of foil, on the grill. Cook until the salmon is just cooked through but still bright pink in the center— depending on the thickness of the salmon, this should take between 7 and 10 minutes.
When the salmon is almost finished cooking, slather it with the rest of the glaze and let it melt into the fish.
When the fish is fully cooked, transfer it from the foil to a platter and garnish with the fresh chives or parsley.