Pandas Dataframe To Dictionary With Conditions

I have this small dataframe:

PROCESS PROCEDURE   SUB_PROCEDURE
---------------------------------
      A       NaN              S1
      B        P1              S2
      C        P2              S3
      D       NaN              S4

I would like to obtain a dictionary that, if the value in column 'PROCEDURE' is empty, the key, value pair consists of

PROCESS: SUB_PROCEDURE 

and if there is something in the 'PROCEDURE' column:

'PROCESS' : {'PROCEDURE': SUB_PROCEDURE}.

This is how it would show for the above dataframe:

desired_output = {
    'A': 'S1',
    'B': {'P1': 'S2'},
    'C': {'P1': 'S2'},
    'D': 'S4'
} 

This is what I've tried so far:

df_so.set_index('PROCESS')[['PROCEDURE', 'SUB_PROCEDURE']].to_dict()

Use dict comprehension with if condition:

desired_output = {a: {b:c} if pd.notna(b) else c  for a, b,c in df.to_numpy()}
print (desired_output)
{'A': 'S1', 'B': {'P1': 'S2'}, 'C': {'P2': 'S3'}, 'D': 'S4'}