Pat scallops dry and place on a paper towel-lined plate. Let them sit uncovered in the refrigerator while you prepare the sauce. This will allow them to dry out a bit.
Place the orange juice, shallot and a good pinch of salt together in a small saucepan and bring to a boil. Let boil for 10 minutes or so until the liquid has reduced to about 2-3 tablespoons; it should be syrupy. Strain the juice into a clean pan and set aside, covered.**
Season the scallops on both sides with salt and pepper. Dredge them in the flour.
In a heavy skillet set on medium-high heat; when hot, add the softened butter. When the butter stops foaming, add the scallops and cook until nicely browned on the bottom, about 2-3 minutes.
While the first side is browning, reheat the blood orange reduction over medium heat. Flip the scallops.
Whisk the chilled butter into the blood orange reduction, one tablespoon at a time. Divide among two plates.
Place four scallops on each plate of sauce, and serve immediately.