Heat 2 Tbsp. vegetable oil in a large Dutch oven or other heavy pot over medium-high. Season 2 lb. pork shoulder (Boston butt), cut into 1" cubes, all over with kosher salt. Working in 2 batches, cook pork until well browned on all sides, 5–8 minutes per batch (there should be sufficient oil in pot after first batch, but add up to 1 Tbsp. more if pot looks dry). Return all of the pork to pot.

Place racks in top and middle of oven and heat broiler. Arrange 1 bunch scallions, trimmed, 2 large jalapeños, stems removed, halved lengthwise, 1 lb. poblano chiles (about 5 medium), stems removed, halved lengthwise, and 1 lb. tomatillos (about 10 medium), husks removed, rinsed, on a large foil-lined rimmed baking sheet; broil until charred all over, 5–8 minutes.

Transfer vegetables to a food processor. Add 4 garlic cloves, 2 tsp. sugar, 1 tsp. dried oregano, 1 tsp. ground cumin, and a big pinch of salt and process until a coarse purée forms.

Preheat oven to 350°. Set 1 cup purée aside. Pour remaining purée over pork in pot and bring to a simmer over medium-high heat. Cover pot and transfer to oven. Cook, stirring halfway through, until pork is very tender and sauce is thickened, 70–80 minutes.

Just before ragù is done, cook 12 oz. rigatoni in a large pot of boiling salted water, stirring occasionally, until al dente; drain.

Add pasta to ragù and add reserved purée. Cook, stirring, until pasta is coated. Taste and season with salt if needed.

Divide pasta among shallow bowls; top with crumbled Cotija cheese, cilantro leaves, and thinly sliced jalapeño.