Remove long, thin tenders (tenderloins) from side of each chicken breast half and save for another use. Working with one breast at a time, set it on a cutting board and place palm of your non-knife hand on top to hold it flat. With a very sharp knife, slice breast in half horizontally into 2 evenly thick halves. "It helps to set the chicken on the edge of the board so you don't rap your knuckles as you slice. Also, stroke the knife through the meat for a clean cut--don't saw it."
Arrange 1 piece at a time inside a 1-gal. resealable freezer bag so it lies flat; smooth out any wrinkles. "This keeps the chicken from sticking to the bottom of whatever you're pounding with. And the bag is sturdier than plastic wrap." Pound chicken with flat side of a meat mallet or bottom of a sturdy medium frying pan until evenly 1/4 in. thick. "You don't need to bash it. You just gently want to coax it into the right shape. Try to move laterally rather than straight up and down." Repeat with remaining chicken pieces, then season them with salt and pepper.
If cooking on charcoal, light a full chimney of charcoal. When charcoal is evenly lit and covered with gray ash, pour out and arrange coals on one side of firegrate. Set cooking grate in place, cover grill, and let preheat 5 minutes. If cooking on gas, preheat to high (550° to 600°).
Whisk garlic, thyme, parsley, mustard, coriander, and lemon juice together in a large bowl. Drizzle in oil, whisking. Season to taste with salt and pepper. Transfer half of vinaigrette to another container.
Add chicken to large bowl and turn pieces to thoroughly mix. "With the lemon juice, don't let it sit too long, or it will make the texture kind of chalky."
On charcoal grill, when grill is hot, arrange chicken pieces directly over coals (on gas grill, arrange anywhere on cooking grate). Cover and cook, rotating pieces occasionally (but not flipping them), until chicken is almost completely cooked through and only a few pink spots remain on top, 3 to 4 minutes. "You want to get deep, even browning on the outside, because that's flavor, but you don't want to overcook the middle. So I cook them 90 percent of the way through on one side." Flip chicken and cook on second side until just done, about 30 seconds. "This keeps them from overcooking."
Transfer to a serving platter. Rewhisk reserved vinaigrette and pour over chicken. Serve immediately.
*Use a mortar and pestle or a clean spice grinder. Freshly ground seeds deliver the brightest flavor.