Define your own roll
We can create a function that takes a window size argument w and any other keyword arguments.  We use this to build a new DataFrame in which we will call groupby on while passing on the keyword arguments via kwargs.
Note: I didn't have to use 
stride_tricks.as_strided but it is succinct and in my opinion appropriate.
from numpy.lib.stride_tricks import as_strided as stride
import pandas as pd
def roll(df, w, **kwargs):
    v = df.values
    d0, d1 = v.shape
    s0, s1 = v.strides
    a = stride(v, (d0 - (w - 1), w, d1), (s0, s0, s1))
    rolled_df = pd.concat({
        row: pd.DataFrame(values, columns=df.columns)
        for row, values in zip(df.index, a)
    })
    return rolled_df.groupby(level=0, **kwargs)
roll(df, 2).mean()
       Open      High       Low    Close
0  133.0350  133.2975  132.8250  132.930
1  132.9325  133.1200  132.6750  132.745
2  132.7425  132.8875  132.6075  132.710
3  132.7075  132.7875  132.6000  132.720
We can also use the pandas.DataFrame.pipe method to the same effect:
df.pipe(roll, w=2).mean()
OLD ANSWER
Panel has been deprecated.  See above for updated answer.
see https://stackoverflow.com/a/37491779/2336654
define our own roll
def roll(df, w, **kwargs):
    roll_array = np.dstack([df.values[i:i+w, :] for i in range(len(df.index) - w + 1)]).T
    panel = pd.Panel(roll_array, 
                     items=df.index[w-1:],
                     major_axis=df.columns,
                     minor_axis=pd.Index(range(w), name='roll'))
    return panel.to_frame().unstack().T.groupby(level=0, **kwargs)
you should be able to:
roll(df, 2).apply(your_function)
Using mean
roll(df, 2).mean()
major      Open      High       Low    Close
1      133.0350  133.2975  132.8250  132.930
2      132.9325  133.1200  132.6750  132.745
3      132.7425  132.8875  132.6075  132.710
4      132.7075  132.7875  132.6000  132.720
f = lambda df: df.sum(1)
roll(df, 2, group_keys=False).apply(f)
   roll
1  0       532.345
   1       531.830
2  0       531.830
   1       531.115
3  0       531.115
   1       530.780
4  0       530.780
   1       530.850
dtype: float64