In a small bowl, scramble egg. Open and remove the wrapping (not the white rind) and dip into egg mixture.
Coat the brie evenly with Panko breadcrumbs, pressing crumbs into brie. Roll ends in breadcrumbs as well. Set aside.
Drizzle medium-sized pan with olive oil and heat over medium-high heat until oil is hot. Place brie in pan and fry for several minutes until the breadcrumbs are golden brown. With brie up on its end, gradually rotate brie until ends are cooked, then flip over and cook the other side. Remove from heat and set on serving board.
Heat apricot preserves in a pan on low heat (or microwave for 30 seconds at a time). Stir in diced apricots. Pour apricot mixture over brie and serve immediately.
