Wash the rice, then cook the rice according to package instructions. This should take about 20 minutes. When the rice is cooked, gently mix in the cilantro, lime zest, lime juice and salt.
Arrange the scallops on a plate and pat both sides very dry with paper towel. Excess moisture will cause the scallops to steam instead of sear. Season both sides of each scallop with salt and pepper.
Heat a large non-stick frying pan over medium-high heat. Add the olive oil to the pan then add scallops in a single layer and cook 2 minutes until well browned, then carefully flip. Cook the second side for 30 seconds, until a golden brown crust forms and the centers are slightly translucent. Transfer the scallops to a clean plate to hold.
Return pan to medium heat and add ginger and cook about 15 seconds until fragrant. Careful not to burn the ginger! Add apricot jam and soy sauce, stir until combined and heated through. Add in the butter and stir to melt. If the sauce is too thick, stir in 1-2 tablespoons of water to thin the sauce. Turn off heat.
Serve scallops over rice with a drizzle of apricot sauce.