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1
Put the potatoes in a saucepan and add enough water to cover generously.
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2
Salt the water, bring it to a simmer over medium heat, cover partially, and cook until the potatoes are tender enough to stick a fork into but still on the firm side of done, about 20 minutes.
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3
Drain the potatoes and let cool.
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4
(You can boil the potatoes up to a day ahead of time and keep them in the refrigerator if you like.)
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5
While the potatoes are cooking, clarify the butter: Heat the butter in a small skillet over medium heat until it foams and starts to turn dark blond on top, 3 to 5 minutes.
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6
Remove from the heat and let the butter sit for a few minutes.
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7
Then tilt the skillet toward you and gently spoon off and discard the layer of foam.
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8
Pour the clear golden butter into a bowl, discarding the dark dregs at the bottom of the skillet.
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9
Coarsely grate the potatoes, skins and all, onto a baking sheet, making sure to keep them loose and not to pack them down.
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10
Combine 1/2 teaspoon salt and the black pepper in a small bowl.
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11
Heat a 10-inch cast-iron skillet over medium-high heat, and add half of the clarified butter.
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12
Add a third of the potatoes in an even layer, keeping them loose.
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13
Top with half of the onions and season with some of the salt and pepper mixture.
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14
Add another third of the potatoes and the rest of the onions, and season again with salt and pepper.
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15
Add the remaining potatoes, season again, and then reduce the heat to medium and cook the potato cake until the bottom turns dark amber brown, about 15 minutes.
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16
(Peek on the sides: If it's browning too quickly, turn the heat down to medium-low.)
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17
Put a large plate upside down over the skillet, and using two thick oven mitts, grab the sides of the skillet and turn it upside down, releasing the hash-brown cake onto the plate.
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18
Put the empty skillet back on the burner and add all but 1 tablespoon of the remaining clarified butter.
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19
Slide the potato cake back into the skillet.
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20
Cook until the underside turns dark amber brown, 10 to 15 minutes.
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21
While the potato cake is cooking, fry the peppers: Heat a large saute pan over medium heat and add the remaining tablespoon of the clarified butter.
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22
Add the peppers and 1/4 teaspoon salt, and cook, flipping them often, until they blister and feel tender throughout, about 10 minutes.
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23
To serve, lay the large plate upside down over the skillet, and using oven mitts, invert as before.
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24
(If the first side was prettier, invert the cake again onto another serving plate.)
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25
Top with a jumble of fried peppers.
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26
Cut into wedges and serve immediately.
