Place dried tomatoes in a small bowl. Cover with boiling water. Soak for 30 minutes. Brush onion with some of the olive oil. Place onion slices on a grill rack directly over medium-hot coals for 12 to 16 minutes or until both sides are slightly charred, turning once. Set aside.
Using a serrated knife, thinly slice the chilled Brie. Drain and rinse tomatoes. Brush one side of each slice of bread with remaining oil, placing bread slices oiled sides down on waxed paper.
Arrange half of cheese slices on two of the bread slices (oiled sides down). Top cheese with onion, tomatoes, and almonds. Top with remaining cheese and bread slices (oiled sides up). Press gently to keep ingredients from spilling out during grilling.
Carefully place sandwiches on the grill rack directly over medium-hot coals. Grill for 2 to 3 minutes per side or until the cheese is just melted and the bread is toasted.
To serve, cut each large sandwich in half. Garnish cut sandwich halves with fresh basil sprigs, if desired. Serve immediately. Makes 2 large sandwiches (4 servings).