Prepare the ingredients as indicated. Make tamarind juice by starting with 1 Tbs. of compressed tamarind in 1/3 cup of warm water. Work the tamarind with your fingers to dissolve the soft fruit; gather up remaining undissolved pulp, squeeze to extract juice and discard. Add more tamarind or water as necessary to make 1/4 cup of concentrate
Divide the ingredients into two batches and make each batch as follows. Using a large clay mortar with a wooden pestle, pound the garlic and chillies to a paste. Add the dried shrimp and long beans and pound to bruise. Follow with the green papaya and carrot. Stir well with a spoon and pound to bruise the vegetables so that they absorb the heat and flavor of the chillies and garlic.