Brine the Scallops - In a medium bowl, combine salt and hot water. Stir until the salt is mostly dissolved. Add ice cubes, and once the water is cold, add the scallops. Brine for 10 minutes.
Rinse and Dry the Scallops - Drain and rinse the scallops under cold water. Transfer to a sheet pan lined with paper towels. Place another sheet of paper towel on top and gently press until each piece is dry. The drier the scallops, the better the sear.
Season with Salt - Allow the scallops to sit for 10 minutes at room temperature before cooking. Right before cooking, lightly season both sides with salt.
Cook the Scallops - Heat a large 12-inch pan over medium-high heat. Add olive oil. Once hot, add the scallops in a single layer. Gently press on them with a spatula so they make direct contact with the pan. Sear until golden brown on the surface, not moving them, about 3 minutes.
Baste the Scallops - Add butter to the pan and allow it to melt. Flip the scallops and use a spoon to baste, tilting the pan as needed. Cook until firm but tender, about 1 to 2 minutes. Turn off the heat and transfer to a clean plate.
Make a Pan Sauce - Using the same pan to cook the scallops, turn the heat up to medium. Add in garlic and saute until fragrant, 30 seconds. Add in lemon juice and lemon zest, scrape the pan to move any browned bits, and stir them into the sauce, cook for about 1 minute. Turn off the heat and whisk in Dijon mustard and heavy cream. If needed, add some water if you want a thinner consistency. Taste and season with salt and pepper as desired.
To Serve - Add the scallops back to the pan and warm them over low heat for 2 minutes. Garnish with chopped dill and black pepper, and serve.
Notes
Scallop Selection: Dry sea scallops are used for their sweet and briny flavor and ability to form a golden brown crust.
Using Wet Scallops: Add about 1 teaspoon of lemon juice to the brine to remove some of the chemicals and mask the soapy taste.
Scallop Size: Use jumbo scallops, 8 to 10 pieces per pound (about 2 ounces per scallop), or smaller scallops that are 14 to 16 per pound (about 1 ounce per scallop). Adjust cooking times based on size after flipping them.
Storing: Refrigerate in an airtight container for up to 2 days.