Here is the Harbor Freight link for "plug Cutters". Great addition to the tool box. Just use them like a drill and cut around the broken screw. Be sure to go deeper than the screw (?).Then with a small chisel or screwdriver snap out the plug complete with the screw and glue in the proper size dowel. Works every time, Chap
https://www.harborfreight.com/catalo...&q=plug+cutter