Chile-Braised Pork Shoulder Tacos

Place chiles, sugar, lime juice, and 1/4 cup reserved soaking liquid in a blender.

Purée chile mixture, adding more soaking liquid as needed to form a smooth paste.

Season pork shoulder generously with salt and spread paste over pork.

DO AHEAD: Can be rubbed 1-2 days ahead.

Cover and chill.

Let come to room temperature before continuing.

Heat oil in a large heavy pot over medium heat.

Add onion, garlic, bay leaves, oregano, coriander, cumin, and allspice.

Cook, stirring often, until onion is soft, about 8 minutes.

Add beer; bring to a boil.

Add pork to pot; cover and transfer to oven.

Braise pork, basting occasionally with pan juices, until very tender, about 2 1/2 hours.

DO AHEAD: Can be made 2 days ahead.

Let cool slightly.

Chill uncovered until cold, then cover and keep chilled.

Rewarm before continuing.

Transfer pork to a large platter.

Let cool slightly.

Pour pan juice mixture over pork; cover and keep warm. (Alternatively, shred the pork with 2 forks and pour pan juice mixture over pork.).

Meanwhile, working in batches, cook tortillas in a large heavy skillet over low heat until toasted, about 1 minute per side.

Transfer to a large sheet of foil; wrap to keep warm.

Serve pork with tortillas, radishes, both salsas, pickled onions, and chopped cilantro, encouraging guests to fill and garnish tacos as desired.