Preheat the oven to 325 degrees F. Rub the pork on all sides with 1 tablespoon salt and 1 teaspoon pepper; set aside.
Heat the olive oil in a large Dutch oven or heavy-bottomed pot over medium-high heat. Add the pork and brown it on all sides, 5 to 10 minutes. Place the pork in the pot with the fat side facing up, and then pour in the tomatillo salsa and chicken broth.
Bring the mixture to a simmer, cover the pot and transfer to the oven. Cook until the meat pulls apart easily and the internal temperature on an instant read thermometer reads 185 degrees F, about 3 hours. Use 2 forks to shred the pork into smaller pieces, then stir in the white beans and cilantro. Salt and pepper the shredded pork to taste.
Increase the oven temperature to 375 degrees F. Line a baking sheet with parchment paper; set aside.
On a lightly floured surface, roll out the pizza dough to about 1/4 inch thick, 15 inches long and 9 inches wide, then cut into 3 long 3-inch-wide strips. Evenly spread 1 cup of the pork and bean mixture along the long edge of a dough strip. Sprinkle about 1/4 cup cheese over the pork mixture, then carefully roll up the dough to enclose the filling. Arrange the dough seam-side down on the prepared baking sheet in a curved and winding pattern to look like intestines. Repeat the process with the remaining dough and filling. Reserve the remaining pork mixture for another use.
In a small bowl, use a whisk to beat the egg and tomato paste together until completely combined. Brush the dough with the egg wash. Bake until crisp and cooked through, about 25 minutes.