Process shallots, garlic, chilli, shrimp paste, if using, and sugar in a food processor until a smooth paste forms. Transfer to a bowl with kecap manis, tamarind paste and oil. Stir to combine.
Place chicken, breast-side down, on a chopping board. Use kitchen scissors to cut down either side of the backbone to remove. Turn chicken over and press down breastbone to flatten. Rub chicken all over with lime juice and season. Place in the fridge for at least 30 mins to develop the flavours.
To make pickled vegetables, combine vinegar and sugar in a saucepan over medium heat. Stir until sugar dissolves. Bring to the boil. Place radish, cucumber, carrot and chilli in a jar. Pour hot pickling liquid over vegetables. Set aside at room temperature for 1 hour to cool. Place in the fridge to chill until ready to serve.
Preheat oven to 200°C. Place the chicken, breast-side up, in a roasting pan. Rub all over with butter. Roast for 15 mins. Reduce oven to 180°C. Roast for 35 mins or until the skin begins to brown. Spoon shallot mixture over chicken and roast for 20 mins or until caramelised.
Transfer chicken to a serving platter and serve with pickled vegetables.
Serve with lime wedges and coriander.