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1
To peel the watermelon, slice off both ends to reveal the flesh.
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2
Stand the watermelon upright on the cutting board.
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3
Using a large knife, slice the rind from the flesh, working from the top to the bottom in one long slice if possible.
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4
Repeat, using the white of the rind as a guide for the knife, until the melon is completely peeled.
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5
Cut the flesh into 2-inch-thick slices and set aside the rounded end cuts.
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6
Trim the slices into shapes that will fit on the serving platter you plan to use.
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7
Reserve the heart (center) of the melon.
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8
Season each slice with salt and, using 1/4 cup of the olive oil, brush one side of each slice.
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9
Heat a large skillet or griddle over medium heat.
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10
When hot, working in batches, place the watermelon slices, oiled side down, on the hot skillet and leave for about 45 seconds, or until heated.
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11
With a large spatula or tongs, remove the slices, heated side up, to a chilled plate.
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12
Put the reserved heart of the melon and the rounded end pieces in a sieve over a bowl and smash your hands on a stiff whisk, forcing the juice into the bowl.
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13
Measure 1 cup of the juice (drink the rest or freeze it into ice cubes).
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14
In a saucepan, combine the vinegar and watermelon juice.
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15
Bring to a boil over medium-high heat, reduce the heat to medium, and simmer, uncovered, for about 15 minutes, or until reduced to about 1/4 cup.
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16
Pour the reduced juice into a serving bowl and whisk in the remaining 1/4 cup oil.
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17
Season to taste with salt and pepper.
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18
Add the arugula, almonds, scallions, and radishes and toss well.
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19
Gently mound the arugula salad over the melon slices and serve.
