In a food processor, combine scallions, chiles, garlic, ginger, lime juice, soy sauce, sugar, pumpkin-pie spice, and thyme; puree into a thick paste. Set aside.
To butterfly chicken: Using a knife or poultry shears, cut out the backbone. With a heavy pot, crack breastplate so the bird lays flat. Place butterflied chicken in a gallon-size resealable plastic bag. Rub reserved paste over chicken, and seal bag. Refrigerate for 12 hours (or up to 1 day).
Heat grill to medium-low; lightly oil grates. Wipe chicken with paper towels to remove excess paste, and season with 1 tablespoon coarse salt. Place, skin side down, on grill and cook, turning occasionally, until lightly charred and an instant-read thermometer inserted in thickest part of a thigh (avoiding bone) registers 165 degrees, 35 to 40 minutes (if browning too quickly, move to a cooler part of grill). Let rest 5 minutes before serving.
Butterflying reduces the bird's cooking time -- ask your butcher to do it, or see step 2. To give the meat big taste, puree the marinade ingredients into a smooth paste. Plenty of (hands-off) marinating time deepens the flavor.