Place shallots, lemongrass, garlic, ginger, galangal, and chile peppers in a food processor; process spices into a coarse paste.
Heat vegetable oil in a large pot over medium heat. Add spice paste; cook and stir until sizzling and fragrant, 3 to 5 minutes. Stir in curry powder and cook until fragrant, about 1 minute. Add beef; stir to coat with spices, about 3 minutes. Pour in coconut milk. Cover and simmer stew until beef is tender, about 30 minutes.
Stir vinegar, sugar, and salt into the pot. Continue to cook, covered, until sauce reduces and thickens, about 30 minutes more.