Tamarind Chipotle-Rubbed Carnitas Tortas

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Carnitas:

1 1/2 pounds boneless pork butt

3 ounces tamarind paste

2 ounces brown sugar

1 ounce canned chipotle chiles

2 cups orange juice

One 12.5-ounce bottle tamarind soda, such as Jarritos

1/2 pound lard

Black Beans:

One 15.5-ounce can black beans, drained and rinsed

2 tablespoons lard

To Serve:

1 cup mayonnaise

4 telera rolls, split

1 red onion, thinly sliced

2 avocados, sliced

1 bunch fresh cilantro, chopped

Vegetable oil, for toasting sandwiches