Blend or pound the shallots and garlic into a rough paste. A few pulses in a small food processor with a splash of water is all it takes. This is the base of the gravy, so it should be smooth enough to melt into the sauce.
Heat the oil in a wide pot or deep skillet over medium heat. Add the shallot garlic paste and fry, stirring often, for 4 to 5 minutes until it smells sweet and the raw edge is gone. Add the mashed taucheo and fry another minute. This step matters. Frying the taucheo until fragrant is what gives pongteh its savory depth, and rushing it leaves the gravy tasting flat.
Add the chicken chunks and turn them in the paste for 2 minutes, just to coat. Stir in the dark soy, light soy, sugar, white pepper, and the shiitake if using.
Pour in the water or stock, enough to almost cover. Bring to a boil, then drop to a gentle simmer, cover, and cook 15 minutes.
Add the potatoes and simmer uncovered for another 20 to 25 minutes, until the potatoes are fork tender and the gravy has reduced by about a third. Nudge the potatoes now and then so they cook evenly and start to thicken the sauce as their edges break down.
Taste and adjust. It should be savory first, gently sweet second. Add a splash of water if it reduced too far, or a pinch more sugar to round it out. Top with fried shallots and spring onion and serve over rice.