class WEBrick::Log

def initialize(log_file=nil, level=nil)

You can set the timestamp format through #time_format

Same as BasicLog#initialize
# 
def initialize(log_file=nil, level=nil)
  super(log_file, level)
  @time_format = "[%Y-%m-%d %H:%M:%S]"
end

def log(level, data)

Same as BasicLog#log
# 
def log(level, data)
  tmp = Time.now.strftime(@time_format)
  tmp << " " << data
  super(level, tmp)
end