Make the curry paste

1. Char turmeric over an open flame until black in spots and fragrant, about 30 seconds. Scrape off skin using the back of a paring knife, and slice into 1/8- to 1/4-inch-thick pieces. Slice ginger into 1/8- to 1/4-inch-thick pieces. Grind turmeric, ginger, and 1/2 teaspoon salt into a paste using a large, shallow stone mortar and pestle. Scrape paste to the side. Add nuts, and mash into a paste. Add shallots, garlic, and remaining 1/2 teaspoon salt; mash until liquid releases and mixture resembles a chunky paste. Add long red chiles, and grind into a paste.

2. Bruise pale part of lemongrass, hitting with heel of a chef’s knife; bend stalk, tie into a knot, and set aside. Slice galangal into thick pieces; using pestle, gently smash on cutting board. Crush lime leaves in your hand; add to curry paste.

Make the curry

1. Heat oil in a large Dutch oven over medium. Add curry paste, lemongrass, galangal, bay leaves, cloves, cardamom, cinnamon, star anise, coriander, and cumin; cook, stirring often, until paste darkens and dries, 8 to 10 minutes. Stir in salt.

Make the chicken

1. Add chicken pieces to Dutch oven, turning to coat with paste. Add coconut milk, 1/4 cup water, and sugar; stir well to combine. Bring mixture to a simmer over medium. Reduce heat to medium-low or low, and simmer, uncovered, 15 minutes, adjusting heat as needed to maintain a gentle simmer. Add Thai chiles to Dutch oven. Cook, uncovered, stirring occasionally and flipping chicken pieces once, until an instant-read thermometer registers 165°F when inserted in thickest portions of chicken and coconut milk thickens slightly, 55 minutes to 1 hour and 15 minutes.

2. Remove chicken curry from heat; remove and discard lemongrass, galangal, and bay leaves. Sprinkle with fried shallots; serve alongside steamed jasmine rice and cucumber slices.