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1
Boil potatoes in salted water with 1 sprig of the rosemary and 2 cloves of garlic until tender.
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2
Drain potatoes and discard rosemary and garlic.
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3
Place potatoes on a cutting board and use the side of a cleaver or the bottom of a pot to lightly crush them, keeping them as intact as possible.
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4
Strip leaves from remaining rosemary sprig and chop.
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5
Mince remaining garlic clove.
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6
Place in a dish with lemon juice and zest and whisk in olive oil and chile flakes.
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7
Season with salt.
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8
Heat oven to 200 degrees.
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9
Line a small baking sheet with a couple of layers of paper towels.
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10
Heat grape seed or canola oil on medium-high to a depth of 1/2 inch in a skillet large enough to hold potatoes in a single layer (a 10-inch skillet should work).
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11
When oil is hot, add smashed potatoes and fry, turning once, until golden brown and crusty.
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12
Season with salt, transfer to baking sheet and place in the oven.
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13
Bring an inch or so of water to a simmer in a shallow 2-quart saucepan.
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14
Add vinegar.
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15
Break an egg into a teacup and slip the egg out of the cup and into the water.
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16
Repeat with second egg.
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17
(And with two more eggs if you desire.)
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18
Simmer until just set, about 3 minutes.
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19
Divide potatoes between two warm plates, give the vinaigrette another whisking and drizzle about half of it over the potatoes.
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20
Use a slotted spoon to lift eggs from the water and place onto the potatoes.
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21
Drizzle eggs with the rest of the vinaigrette and serve.
