In a stand mixer, put the yeast, sugar and warm water. Let it sit for a few minutes until it's nice and bubbly. Then add the remaining ingredients except for one cup of the all purpose flour. Using the dough hook of your machine, mix the dough together. The dough will start to come together in a ball, but will be loose. Keep adding flour by the spoonful until the dough no longer sticks to the side and bottom of the bowl. Knead for 4 minutes.
Ready to knead
Flour a working surface with a little flour. Turn the dough onto the surface and knead it by hand a few times. Do the window pane test by pulling some of the dough - it should be nice and elastic and when you can see your finger through it, it is done.
Passed the windowpane test
Pat the dough into a nice round.
Ready to rest
Transfer the dough to a lightly greased bowl or dough-rising bucket, cover the bowl or bucket, and allow the dough to rise until puffy though not necessarily doubled in bulk, about 1 1/2 hours, depending on the warmth of your kitchen.
Lightly grease a 13" pain de mie pan. Gently deflate the dough, transfer it to a lightly greased work surface.
Flatten it and shape it until it is the same length as your pan.
Long as the pan
Shape it into a 13" log, and fit it into the pan.
Resting in the pan
Cover the pan with lightly greased plastic wrap, and allow the dough to rise until it's just below the lip of the pan, 45 minutes to 1 hour, depending on the warmth of your kitchen (it may rise even more slowly in a cool kitchen; don't worry, this long rise will give it great flavor).
Time to bake
Towards the end of the rising time, preheat the oven to 350°F.
Remove the plastic, and place the cover on the pan.
Putting on the top
Bake the bread for 25 minutes. Remove the pan from the oven, and carefully remove the lid.
Take off the top very carefully
Return the bread to the oven to bake for an additional 20 minutes, or until it tests done; a digital thermometer inserted into the center will register 190°F.
Remove the bread from the oven, and turn it out of the pan onto a rack to cool completely.
You will be tempted to eat the bread while it is still warm, but that is not advisable. You can wait, it's worth it!
Notes
For the potato flour, you can put boxed mashed potato flakes in a food processor and grind them until they are a fine powder. Store in a tightly covered in a cool, dry place.
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