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1
Adjust the oven rack to the middle position and preheat the oven to 450F.
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2
Scrub the carrots and trim and discard the stems, leaving the last 3/4 inch of the stems attached.
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3
Place the carrots in a large bowl, drizzle with the olive oil, sprinkle with the salt and pepper, and toss to coat the carrots with the seasonings.
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4
Spread the carrots in a single layer on a baking sheet and place them in the oven to roast until they are golden in spots and tender but not mushy, shaking the pan occasionally during cooking time so they cook evenly, 10 to 15 minutes.
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5
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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6
Heat the oil over medium-high heat until a pinch of salt sizzles when dropped into it.
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7
Add the rosemary and fry for about 30 seconds, until its crisp but not brown.
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8
Use a slotted spoon to remove the rosemary from the oil, transfer to the paper towels to drain, and season with sea salt.
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9
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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10
(The rosemary can be fried up to several hours in advance.
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11
Store it in an airtight container at room temperature.)
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12
Remove the carrots from the oven.
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13
Spoon 1/4 cup of the relish over them and toss gently to distribute the relish.
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14
To serve, place a layer of carrots on a platter and spoon some of the relish remaining on the baking sheet over the carrots.
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15
Build another layer with the carrots perpendicular to the first layer.
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16
Add more of the relish and build a third layer.
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17
Spoon the remaining tablespoon of relish over the carrots and scatter the fried rosemary over and around them.
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18
Serve warm or at room temperature.
