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1
Heat oven to 400 degrees and butter a 9 by 13-inch baking dish and set aside.
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2
Using a mandolin, V-slicer or the slicing attachment on a food processor, slice the potatoes approximately 1/8-inch thick.
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3
(If you don't want to slice all the potatoes at once, slice them one at a time and build the gratin as you go.)
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4
Create the first layer by laying the slices in overlapping rows.
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5
Once the first layer is down, season lightly with salt and pepper, then scatter with mushroom slices and a couple tablespoons of the cheese.
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6
(Don't over-do it on these layers, if you create a barrier between the adjoining potato layers, the gratin won't set.)
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7
Continue building layers until you're out of potatoes or out of room to build, but be sure to save 1/2 cup of the cheese for the top.
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8
Pour 2/3 cup of the half and half over the gratin then spread both hands over the surface and push down to work the air out from the layers.
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9
Add remaining liquid only if half and half does not come to the surface when you push down.
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10
Sprinkle the gratin with cheese, cover loosely with foil and place in middle of oven for 1 hour.
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11
Check for doneness by inserting the point of a paring knife straight into the gratin.
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12
If it goes through smoothly, remove the foil, return to oven, and turn on the broiler just long enough to turn the top golden-brown.
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13
Remove, and allow to sit at room temperature for 15 to 20 minutes before serving.
