Use paper towel to pat chicken very dry. Place breast-side down on a large plastic cutting board. Using very sharp kitchen shears, carefully snip along each side of the backbone, until completely detached. With breast side of the chicken still facing down, use your hands to gently stretch open the rib cavity of the chicken. Place the heel of your knife at the center of the wishbone. Forcefully press down until the wishbone snaps and the breastplate cracks. Slice between the breasts to create two halves.
In a large bowl, whisk together the pineapple juice, brown sugar, ketchup, & 2 Tbsp kosher salt. Transfer 1 cup of the brine to a small airtight container & reserve for basting. Place the halved chicken in a large bowl. Pour the remaining pineapple brine over top, submerging the chicken as much as possible. Cover, then transfer to the refrigerator to brine for at least 12 hours & up to 48 hours.
Add all listed ingredients to a small saucepan over medium-high heat. Season with 1/2 teaspoon kosher salt & whisk to combine well. Once the huli huli sauce comes to a boil, reduce heat to medium-low. Simmer, stirring the sauce occasionally, for 20 minutes to reduce & thicken. Remove from the heat & set aside for serving.
Place the chicken on the indirect heat side of the grill, breast side up, as close to the fire as possible without being over the direct heat. Close the grill lid. Cook the chicken, stopping to rotate it 180 degrees every 15 minutes. With each rotation, use a pastry brush to generously baste the surface of the chicken with the reserved pineapple brine. The chicken is ready once an instant-read thermometer registers a temperature of 160 degrees F.
Remove the huli huli chicken from the grill. Transfer to a large plate & set aside to rest for 5-10 minutes. Carryover heat will cause the internal temperature to continue to rise as it rests. The chicken is be ready to serve once an instant-read thermometer inserted in the thickest part of the chicken (without hitting the bone) registers a temperature of 165 degrees F.