For the Spice Paste: Using scissors or kitchen shears, cut dried chiles diagonally into ¼-inch strips. Using your hands, massage strips gently to release as many seeds as possible into a bowl.

Transfer chile strips without the seeds to another bowl and add the dried shrimp. Cover chile strips and dried shrimp with enough warm water to cover, about 1 cup. Let sit until soft and rehydrated, about 15 minutes.

In a 10-inch nonstick or stainless skillet set over medium heat, toast coriander seeds, cumin seeds, fennel seeds, black peppercorns, and white peppercorns until fragrant and slightly darkened, about 1 minute. Remove from heat and immediately transfer toasted spices to a mortar or spice grinder. Let cool for 1 minute, then pound or grind spices until finely ground. Transfer to a small bowl and stir in chile powder and turmeric; set aside.

In a blender or food processor, combine shallots, garlic, ginger, galangal, turmeric root, red chiles, candlenuts, lemongrass, shrimp paste, and the soaked chile strips and rehydrated dried shrimp. Add ½ cup soaking liquid and ¼ cup oil. Blend until smooth, 3 to 5 minutes.

In the same skillet used for toasting the spices earlier, heat remaining ¼ cup oil over medium heat until shimmering. Add spice paste and ground spices, reduce heat to low, and cook, stirring occasionally, until color deepens to a dark red and oil separates, about 35 minutes. Remove from heat and set aside.

For the Broth: Remove the heads and shells from shrimp; set aside. Place shrimp meat in a medium bowl and refrigerate until ready to use. In a 5-quart pot, heat 2 tablespoons oil over medium heat until shimmering. Add shrimp heads and shells to pot and fry until shells turn bright pink, 3 to 5 minutes, using a spatula or wooden spoon to press the heads to extract all the juices. Add the Vietnamese mint and fry until slightly darkened and fragrant, 1 to 2 minutes, then add 4 cups water.

Bring to a boil over high heat, then reduce heat to low and simmer until fragrant, about 30 minutes. Turn off heat. Using a fine-mesh sieve, strain stock into a large bowl, gently pressing on shells to extract as much liquid as possible. Rinse pot of any stray shells and place pot back on stove.

Pour strained stock back into the pot, and add cooked spice paste, coconut milk, salt, sugar, and tamarind concentrate, and stir until smooth. Bring to a simmer over medium heat, then reduce heat to medium-low. Gently simmer until flavors meld, about 20 minutes. Season to taste with additional coconut milk, salt, sugar, or tamarind concentrate as needed. Add halved soy puffs and cook until soy puffs have absorbed broth, about 10 minutes.

To Assemble: While broth is simmering, prepare laksa components. Bring a medium pot of salted water to a boil. Blanch bean sprouts until tender, about 1 minute; use tongs or a slotted spoon to remove sprouts and set aside in separate bowls. Return water to a boil and blanch long beans until tender, about 5 minutes; use tongs or a slotted spoon and set aside. Blanch shrimp until pink and tender, 2 to 3 minutes; use tongs or a slotted spoon and set aside. Using the same pot, blanch or cook rice noodles until tender and cooked through, about 3 minutes. Using a colander, drain noodles.

Divide noodles and broth equally among 4 bowls; each bowl should have about 4 ounces noodles and about 1 cup broth. Top each bowl with shrimp, bean sprouts, long beans, cucumbers, Vietnamese mint leaves, and half a boiled egg. Serve with calamansi lime halves and sambal.