How to do pandas equivalence of SQL outer join without a key

You can add a column to both dfs with a constant value,

>>>df1['joincol'] = 1
>>>df2['joincol'] = 1
>>>pd.merge(left=df2,right=df1, on='joincol', how='outer')
  Person Type_x  joincol     Food   Type_y
0    ian      *        1    pizza  italian
1    ian      *        1  lasagna  italian
2    ian      *        1   orange    fruit

then delete it afterward when you remove your other undesired columns.