Parse a list of lists into a Sad-List
Pyth, 13 bytes

L+]/bYyM-b]Yy


Test suite.

How it works

L+]/bYyM-b]Yy
L               define a function y with argument b:
   /bY              list 1: count how many [] can be found in b
  ]                         wrap into singleton
        -b]Y        list 2: filter out [] from b
      yM                    apply y (this function) to each
 +                  concatenate the two lists above
            y   apply y to the input