Combine salt and hot water in a medium bowl, stir until the salt is mostly dissolved. Add ice cubes, once the water is cold add scallops. Brine scallops for 10 minutes.
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 of scallops, gently pressing until each piece is dry. The drier the scallops, the better the sear.
Allow scallops to sit for 10 minutes at room temperature before cooking. Right before cooking, lightly season both sides with salt.
Heat a large 12-inch pan over medium-high heat. Add olive oil. Once hot, add scallops to the pan in a single layer. Gently press on them with a spatula so they make direct contact with the pan. Pan sear until golden brown on the surface, not moving them, about 3 minutes.
Add butter to the pan and allow it to melt. Flip scallops over, use a spoon to baste with butter, 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.
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 remove any browned bits and stir into the sauce, cook for about 1 minute. Turn off the heat and whisk in Dijon mustard and heavy cream. If needed, add in some water to the sauce if you want a thinner consistency. Taste and season with salt and pepper as desired.
Add scallops back to the pan, and warm over low heat, 2 minutes. Garnish with chopped dill and black pepper, serve warm.
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 the scallops over.
Using Wet Scallops: If you don’t have the option to purchase dry scallops, just add about 1 teaspoon of lemon juice to the brine and that will help remove some of the chemicals and mask the soapy taste.