Grilled Salmon with Fennel Cucumber Relish

4 cups water
1 1/2 cups packed light brown
3/4 cup kosher salt
1/4 cup granulated sugar
1/2 cup chopped fresh dill
salmon fillet with skin (whole or cut into serving sizes)

1 lb fennel, stalks discarded and bulb finely chopped
1 lb seedless cucumbers, halved lengthwise, cored, and cut into 1/4-inch dice
6 tablespoons cider vinegar, or to taste
2 tablespoons finely chopped shallot
1 1/2 tablespoons chopped fresh dill
1 1/2 tablespoons vegetable oil
1 tablespoon sugar
1/4 teaspoon salt, or to taste

1. Bring water, brown sugar, salt, and granulated sugar to a boil in a pot, stirring until sugar is dissolved. Transfer brine to a heat proof baking dish, then stir in dill and cool. (Brine, without dill, can be made 1 day ahead and kept, covered, at room temperature.)

2. Marinate salmon, skin sides up, in brine in baking dish, chilled, 1 hour. Do not turn salmon and do not marinate for longer than 1 hour.

3. Prepare grill for cooking.

4. Stir together all remaining relish ingredients in a bowl and let stand 15 minutes. Relish can be made 1 day ahead (though color will not be quite as bright) and chilled, covered. Bring to room temperature before serving.

5. Remove salmon from brine and pat dry, discarding brine. 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.