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1
Bring water, brown sugar, salt, and 6 tablespoons granulated sugar to a boil in a 5-quart pot, stirring until sugar is dissolved.
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2
Transfer 6 cups brine to a 13- by 9-inch glass or ceramic baking dish, then stir in dill and cool.
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3
Transfer remaining 4 cups brine to a large bowl and add remaining 4 tablespoons granulated sugar, stirring until dissolved, then cool completely.
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4
Marinate salmon, skin sides up, in brine in baking dish, chilled, 1 hour.
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5
(Do not turn salmon.)
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6
Put eggplant in brine in bowl, then invert a small plate over eggplant and weight it with soup can (to keep eggplant immersed).
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7
Marinate eggplant at room temperature 30 minutes.
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8
(Do not brine salmon or eggplant longer than indicated or they will be too salty.)
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9
Prepare charcoal or gas grill for cooking.
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10
Remove salmon from brine and pat dry, discarding brine.
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11
Remove eggplant from brine, then rinse and pat dry, discarding brine.
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12
Toss eggplant with oil and pepper to taste in a bowl.
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13
When fire is moderate (you can hold your hand 5 inches above rack for 3 to 4 seconds), grill eggplant on lightly oiled grill rack, turning once, until golden, about 4 minutes total.
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14
Transfer to a platter with tongs and keep warm, covered.
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15
When fire is moderately low (you can hold your hand 5 inches above rack for 5 to 6 seconds), grill salmon, starting with skin sides up and turning once, until just cooked through and skin is crisp, about 8 minutes total.
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16
Serve salmon over eggplant.
