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1
Combine the potatoes, chopped rosemary, butter, garlic, salt, and 1/4 cup of the olive oil in a large saute pan over medium heat.
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2
When the butter melts, stir to combine, then cover the pan with a lid and cook the potatoes until they are tender when pierced with a fork, about 30 minutes.
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3
Uncover the pan, remove the potatoes from the pan, and set them aside to cool slightly.
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4
Remove the garlic with a slotted spoon and discard, reserving the oil and butter in the pan.
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5
When the potatoes are cool enough to touch, one at a time, place the potatoes on a flat surface and use the heel of your hand to smash them 1/2 inch thick, pressing evenly to prevent the potatoes from breaking apart.
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6
Slide the potatoes off the surface rather than lifting them, to help keep them intact.
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7
You can prepare the potatoes to this point up to several hours in advance.
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8
Proceed just before you are ready to serve them.
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9
Add 2 tablespoons of the remaining olive oil to the oil-butter mixture, or enough so the fat in the pan is 1/2 inch deep, and heat over medium-high heat until the oil is almost smoking and slides easily in the pan, 2 to 3 minutes.
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10
If the oil begins to bubble, reduce the heat slightly.Working in two or more batches, add the smashed potatoes in a single layer to the pan, season with salt, and cook until they are deep brown and crisp, about 3 minutes per side.
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11
Remove the potatoes to paper towels to drain and season them with sea salt.
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12
Add the remaining 2 tablespoons of oil to the pan, or more as needed, and heat before adding the second batch.
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13
Cook the remaining potatoes in the same way.
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14
To fry the rosemary, pour enough olive oil into a small skillet or saucepan to fill it 1 inch deep and line a small plate with paper towels.
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15
Heat the oil over medium-high heat until a pinch of salt sizzles when dropped into it.
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16
Add the rosemary and fry for about 30 seconds until crisp but not brown.
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17
Use a slotted spoon to remove the rosemary from the oil, transfer to the paper towels to drain, and season with salt.
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18
Strain the rosemary-infused oil through a fine-mesh strainer and reserve it to fry rosemary another time, to make vinaigrettes, or to drizzle over grilled meats or vegetables.
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19
(The rosemary can be fried up to several hours in advance.
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20
Store it in an airtight container at room temperature.)
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21
Serve warm, with the fried rosemary branches scattered on top.
