Step 1

Whisk water and salt in large bowl until salt is dissolved. Add zucchini to brine and weigh down with plate to keep submerged. Let sit at room temperature for at least 45 minutes or up to 1 hour. Transfer zucchini to paper towel–lined plate and pat dry. Discard brine.

Step 2

For a Charcoal Grill: Open bottom vent completely. Light large chimney starter filled with charcoal briquettes (6 quarts [4½ pounds]). When top coals are partially covered with ash, pour evenly over half of grill. Set cooking grate in place, cover, and open lid vent completely. Heat grill until hot, about 5 minutes. For a Gas Grill: Turn all burners to high, cover, and heat grill until hot, about 15 minutes. Leave all burners on high.

Step 3

Clean and oil cooking grate. Place zucchini, cut side down, on grill (directly over coals if using charcoal) and cook until zucchini are well charred on bottom and flesh just begins to soften, 3 to 4 minutes. Flip zucchini and continue to cook until skin side is charred, about 2 minutes longer. (Zucchini should be slightly soft at edges but still firm at centers.) Transfer to serving plate.

Step 4

Stir together mint, parsley, oil, vinegar, capers, garlic, and pepper flakes in small bowl. Season with salt to taste. Spoon salsa verde over zucchini and serve.