In a 3-quart saucepan, combine potatoes and salt and cover by 2 inches with water. Bring to a boil over medium-high heat, reduce heat to a simmer, and cook until potatoes are just tender, offering little resistance when poked with a paring knife, about 10 minutes. Drain potatoes and set aside; return saucepan to stovetop.

While potatoes cook, in a small bowl, whisk together ½ cup (120ml) coconut milk and ½ cup (120ml) water; set thinned coconut milk mixture aside.

In now-empty saucepan, bring ½ cup (120ml) coconut milk to a boil over medium heat, and cook until slightly thickened, about 2 minutes. Add curry paste and stir vigorously with a rubber spatula to combine, scraping sides of saucepan to fully incorporate paste. Raise heat to medium-high and cook, stirring and scraping constantly until paste mixture begins to spit, about 1 minute. Lower heat back to medium and continue to cook while gradually adding remaining ½ cup (120ml) coconut milk in 2-tablespoon (30ml) increments, until paste turns dark red and fat begins to separate from curry paste, 8 to 10 minutes.

Add palm sugar, soy sauce, and reserved thinned coconut milk mixture, and stir until palm sugar is fully dissolved. Bring to a simmer, add potatoes, eggplant, and cherry tomatoes, and cook, stirring occasionally, until eggplant is tender, 5 to 7 minutes. Remove from heat.

Transfer curry to a large serving bowl or divide between individual bowls and top with fried shallots. Serve immediately with cooked jasmine rice.