The direct answer is that it doesn't appear to be possible with Matplotlib to set multiple radii within the same pie plot.
#! /usr/bin/env python
# -*- coding: utf-8 -*-
import matplotlib.pyplot as plt
data = [4, 3, 2, 1]
fig, ax = plt.subplots(figsize=(4,4))
wedges, texts = ax.pie(data, radius=1)
for w in wedges:
w.set_width(.5)
wedges[0].set_radius(1.1)
wedges[1].set_radius(1)
wedges[2].set_radius(1)
wedges[3].set_radius(1)
plt.show()
radii = [w.radius for w in wedges]
print(radii)
We can see that the radii are, in fact, different.
[1.1, 1, 1, 1]
But Different Radii Don't Appear to be Different

An interesting side note is that slice widths can be different:
Slices with Different Widths

Another Way
However, you can work around this with a little bit of sleight of hand. Instead of plotting one pie plot, you plot two--the first with the "enlarged" slice invisible and the second plot with the "enlarged" slice set as the only visible slice.
#! /usr/bin/env python
# -*- coding: utf-8 -*-
import matplotlib.pyplot as plt
data = [4, 3, 2, 1]
fig, ax = plt.subplots(figsize=(4,4))
# Pie 1
wedges, texts = ax.pie(data, radius=1)
for w in wedges:
w.set_width(.5)
wedges[0].set_visible(False)
# Pie 2
wedges1, texts1 = ax.pie(data, radius=1.1)
for w in wedges1:
w.set_width(.6)
wedges1[1].set_visible(False)
wedges1[2].set_visible(False)
wedges1[3].set_visible(False)
plt.show()
Example of Pie Plot with Enlarged Slice

The set_width arguments are added to make the plot a "donut" plot like your example. Note the width values in each chart that are required to achieve the desired look.