Stir salt and water in a medium bowl. Add scallops and let stand for 10 minutes. Drain scallops, rinse with cold water, then lay and pat on paper towels. Be sure to dry very thoroughly. Remove as much water as possible. Let scallops dry for at least 15 minutes before cooking.
In a 12-inch sauté pan or cast iron skillet, heat olive oils over medium-high heat until oil just begins to shimmer.
Place scallops into the hot pan without crowding. Gently press scallops with spatula to make contact with the pan. If you didn’t dry them well enough, it will create a bit of a splatter mess, so have a screen handy just in case.
Sear scallops without moving them, continuing to cook until bottoms are a rich golden brown, 3 to 3 ½ minutes.
Turn the scallops over and cook the second side.
When the scallops are opaque in color and firm to the touch, about 1 to 2 minutes, transfer to a plate.
In the same pan reduce heat to medium. Add garlic and shallots and cook for 1 minute until fragrant, not brown.
Increase heat to medium-high and add wine. Simmer wine, stirring as needed until the wine is reduced by half, about 3 minutes.
Turn heat to high and add the chicken stock, lemon zest, lemon juice and capers to the pan. Cook until sauce is reduced by half, about ½ cup, 8 to 10 minutes.
Turn off heat and whisk in Dijon mustard.
Turn heat to medium and add scallops back to pan, cook until warm, 2 minutes.
Taste sauce and season with salt and pepper as needed.
Garnish scallops with chives, dill and or lemon wedges. Serve with rice, risotto or pasta.