Preheat the oven to 450°F (235°C). Line a rimmed baking sheet with foil. Place oxtails on the pan and drizzle with 1 tablespoon oil; toss to coat and space out evenly.

Roast the oxtails in the preheated oven for 25 minutes.

For the curry base, add shallots, garlic, ginger, galangal, jalapenos, and Fresno chilies to a food processor and process until a fine paste forms.

Heat the remaining 2 tablespoons of oil in a large Dutch oven over medium-high heat. Add the curry base, and cook, stirring occasionally, until mixture dries out and begins to toast onto the bottom of the pan, 4 to 5 minutes.

Season with salt, coriander, turmeric, chili flakes, nutmeg, and cardamom, and cook, stirring, for 1 minute more. Add coconut milk, tamarind paste, brown sugar, and lemongrass. Stir, scraping the bottom of the pan to deglaze, then pour in beef broth to deglaze.

Add oxtails and enough water to just cover the meat. Increase heat to high until sauce just starts to boil, then reduce to low. Cover and simmer until meat can easily be pulled off the bone, 4 to 6 hours.

Set the oven to 150°F (66°C). Transfer oxtails to an ovenproof pan, and place in the oven to keep warm.