Serves 3
½ teaspoon kosher salt, plus more to taste
¼ teaspoon black pepper
½ cup seeded and finely chopped pickled hot cherry peppers, plus 6 tablespoons pickle brine (from 1 [22.2-ounce jar), divided (if packed in oil, can use oil from peppers instead of olive oil for sautéing mushrooms and use 5 tbsp of brine from hot mixed pickles).
3 tablespoons olive oil
3 cups coarsely chopped trimmed mixed fresh mushrooms (such as oyster, shiitake, and cremini mushrooms) (from 8 ounces whole mushrooms)
1 small (6-ounce) yellow onion, finely chopped (1 cup)
1 medium-size (9-ounce) red bell pepper, chopped (1 1/2 cups)
2 tablespoons minced garlic (about 6 garlic cloves)
1 cup dry white wine
2 (28-ounce) cans whole peeled San Marzano plum tomatoes, finely crushed by hand
½ teaspoon dried oregano
1 pound uncooked rigatoni pasta
1 cup heavy whipping cream
Pecorino Romano cheese, grated with a Microplane grater
Heat oil in a large Dutch oven over medium-high. Add mushrooms; cook, stirring occasionally, until browned in spots, about 8 minutes. Reduce heat to medium. Add onion; cook, stirring often, until onion softens, about 4 minutes. Add bell pepper, garlic, and chopped cherry peppers; cook, stirring often, until fragrant, about 1 minute.
Add wine and pickle brine to mixture in Dutch oven, scraping up any browned bits on bottom. Return mixture to a simmer over medium-high. Simmer, stirring occasionally, until reduced by half, about 2 minutes. Add tomatoes and juices, oregano, and chicken; bring to a boil over medium-high. Reduce to a gentle boil over medium; cook, stirring occasionally, until chicken is tender, tomato mixture thickens, and a spoon leaves a trail when dragged across bottom of pot, about 45 minutes, reducing heat as needed to maintain a gentle boil.
Meanwhile, cook pasta in boiling, salted water according to package directions for al dente. Drain pasta, reserving 1 cup cooking water. Set aside.
Add cream and remaining 3 tablespoons pickle brine to tomato mixture in Dutch oven; stir until combined. Stir in cooked pasta. Cook over low, stirring constantly, until tomato mixture clings to pasta, about 2 minutes. Season with additional salt to taste. Stir in reserved pasta cooking water as needed, 1/4 cup at a time, to loosen sauce as desired. Divide pasta evenly among 8 shallow bowls. Garnish bowls with cheese, and serve.