I've built two mantels that are similar to the one you described. My mantels were about 9ft in length and 6" in depth (including cove moulidng). In each case I attached a 2x6 to the brick using 1/2" split lead anchors attached with lag bolts on about 10" centers. I then assembled the mantel, cove moulding, and bottom and attached the assembly to the 2x6 using either finish nails or countersunk screws with a plug. This approach turned out to be very stable.