Keep indices in Pandas DataFrame with a certain number of non-NaN entires

Lets say I have the following dataframe:

df1 = pd.DataFrame(data    = [1,np.nan,np.nan,1,1,np.nan,1,1,1], 
                   columns = ['X'], 
                   index   = ['a', 'a', 'a', 
                              'b', 'b', 'b',
                              'c', 'c', 'c'])
print(df1)
     X
a  1.0
a  NaN
a  NaN
b  1.0
b  1.0
b  NaN
c  1.0
c  1.0
c  1.0

I want to keep only the indices which have 2 or more non-NaN entries. In this case, the 'a' entries only have one non-NaN value, so I want to drop it and have my result be:

     X
b  1.0
b  1.0
b  NaN
c  1.0
c  1.0
c  1.0

What is the best way to do this? Ideally I want something that works with Dask too, although usually if it works with Pandas it also works in Dask.

from Keep indices in Pandas DataFrame with a certain number of non-NaN entires