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1
Pour 2 tablespoons olive oil into a 12 x 18-inch rimmed baking pan, and spread all over using your fingertips; set aside.
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2
Place half the potatoes in a small saucepan.
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3
Cover with cold water; place over high heat.
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4
Add 3 teaspoons salt when the water comes to a boil.
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5
Reduce heat to medium-high; cook until the potatoes are tender, 10 to 12 minutes.
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6
Drain in a colander, reserving the liquid.
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7
Pass through a potato ricer or a food mill and into a bowl; set aside.
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8
Place 1/4 cup reserved warm liquid into the bowl of an electric mixer fitted with the paddle attachment.
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9
Sprinkle in the yeast, and stir well; let stand until creamy, 5 to 10 minutes.
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10
Add 2 1/4 cups more reserved liquid, 2 tablespoons olive oil, and the reserved mashed potatoes; beat until combined.
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11
In a large bowl, whisk together the flour and remaining 1 1/2 teaspoons salt; add to the potato mixture.
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12
Mix on low speed until the flour is incorporated, about 3 minutes.
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13
Change to the dough hook, and knead on medium-high until the dough is smooth and elastic and is slightly tacky when squeezed but does not stick to your fingers, 4 to 5 minutes.
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14
Turn the dough out onto a clean surface, and knead into a ball.
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15
Place in a lightly oiled large bowl, cover with plastic wrap, and let stand at room temperature until doubled in size, 1 to 1 1/2 hours.
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16
Preheat the oven to 425F.
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17
Spread the dough evenly in the prepared baking pan.
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18
Cover with oiled plastic wrap, and let stand in a warm place until the dough has filled the entire pan and has increased in size by about one-third, about 30 minutes.
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19
Using a mandoline or a knife, slice the remaining potatoes into very thin rounds.
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20
Transfer to a bowl.
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21
Add half the rosemary and 1 tablespoon olive oil; season with salt and pepper.
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22
Toss to coat the potatoes well.
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23
Remove the plastic wrap; dimple the dough with your fingertips, leaving deep indentations.
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24
Drizzle with the remaining 2 tablespoons oil.
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25
Gently press the reserved sliced potatoes into the dough.
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26
Sprinkle with the remaining rosemary.
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27
Bake until golden brown, 30 to 35 minutes.
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28
Remove from the oven; transfer to a wire rack.
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29
Serve warm.
