INSTRUCTIONS
1. For the chicken and rub: Combine lemon zest, salt, and pepper in bowl. Rub zest mixture under chicken skin and tuck wings according to photo 4. Transfer chickens to rack set over rimmed baking sheet and refrigerate, uncovered, for 30 minutes. (Chickens may be prepared up to this point 24 hours in advance; allow chickens to sit at room temperature 30 minutes before grilling.)
2. Heat all burners on high, covered, for 15 minutes. Scrape cooking grate clean and oil cooking grate. Leave primary burner on high and turn all other burners to low. Place lemons over primary burner; place chickens skin side down over cooler part of grill, with legs positioned closest to heat; cover.
3. Adjust primary burner as necessary to maintain temperature of 350 to 375 degrees. Grill lemons until deep brown and caramelized, 5 to 8 minutes. Transfer to bowl. Grill chickens until skin is well browned and breast meat registers 160 degrees, 45 to 55 minutes. Move chickens to hot side of grill and sear, uncovered, until deep brown, 2 to 4 minutes longer.
4. For the vinaigrette: While chickens are grilling, squeeze 1/3 cup juice from grilled lemons into bowl. Using flat side of knife, mash garlic and salt into paste and add to bowl with lemon juice. Stir in mustard, sugar, pepper, and parsley, then slowly whisk in olive oil until emulsified.
5. Transfer chickens to cutting board and let rest 10 to 15 minutes. Carve, transfer to serving platter, and pour 1/3 cup vinaigrette over chicken. Serve, passing remaining vinaigrette at table.