Assemble the sandwiches by layering the ham, brie cheese, apricot preserves, and mustard in equal amounts on two pieces of bread, topping with the remaining two slices of bread. Brush the top of each sandwich with olive oil.
Heat a grill pan over medium heat. Once the pan is hot, lie the sandwiches, oiled side down, in the pan. Brush the top of each sandwich with oil. Cook each side until the bread is golden brown, about 3 minutes per side.