1. To peel the watermelon, slice off both ends to reveal the flesh. Stand the watermelon upright on the cutting board. Using a large knife, slice the rind from the flesh, working from the top to the bottom in one long slice if possible. Repeat, using the white of the rind as a guide for the knife, until the melon is completely peeled. Cut the flesh into 2-inch-thick slices and set aside the rounded end cuts. Trim the slices into shapes that will fit on the serving platter you plan to use. Reserve the heart (center) of the melon. Season each slice with salt and, using 1/4 cup of the olive oil, brush one side of each slice. 2. Heat a large skillet or griddle over medium heat. 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. With a large spatula or tongs, remove the slices, heated side up, to a chilled plate. 3. 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. Measure 1 cup of the juice (drink the rest or freeze it into ice cubes). 4. In a saucepan, combine the vinegar and watermelon juice. 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. 5. Pour the reduced juice into a serving bowl and whisk in the remaining 1/4 cup oil. Season to taste with salt and pepper. Add the arugula, almonds, scallions, and radishes and toss well. Gently mound the arugula salad over the melon slices and serve. ---------------------------------------------------------------------------
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