Grease large dinner plate with vegetable oil spray. Dissolve 1⅛ teaspoons salt and baking soda in 4 teaspoons water in medium bowl. Add pork and fold gently to combine; let stand for 10 minutes.
Add 1 teaspoon garlic, 3/4 teaspoon rosemary, nutmeg, and 3/4 teaspoon pepper to pork and smear with rubber spatula until well combined and tacky, 10 to 15 seconds. Transfer pork mixture to greased plate and form into rough 6-inch patty. Pulse mushrooms in food processor until finely chopped, 10 to 12 pulses.
Heat 2 teaspoons oil in 12-inch skillet over medium-high heat until just smoking. Add patty and cook without moving it until bottom is browned, 2 to 3 minutes. Flip patty and continue to cook until second side is well browned, 2 to 3 minutes longer (very center of patty will be raw). Remove pan from heat, transfer sausage to cutting board, and chop into 1/8- to 1/4-inch pieces. Transfer sausage to bowl and add cream; set aside.
Bring 4 quarts water to boil in large Dutch oven. Add pasta and 2 tablespoons salt and cook, stirring often, until al dente. Reserve 1 1/2 cups cooking water, then drain pasta and return it to pot.
While pasta cooks, return now-empty skillet to medium heat. Add 1 tablespoon oil, mushrooms, and ⅛ teaspoon salt; cook, stirring frequently, until mushrooms are browned, 5 to 7 minutes. Stir in remaining 2 teaspoons oil, remaining garlic, remaining 1/2 teaspoon rosemary, and ½ teaspoon pepper; cook until fragrant, about 30 seconds. Stir in wine, scraping up any browned bits, and cook until completely evaporated, 1 to 2 minutes. Stir in sausage-cream mixture and ¾ cup reserved cooking water and simmer until meat is no longer pink, 1 to 3 minutes. Remove pan from heat and stir in Pecorino until smooth.
Add sauce, parsley, and lemon juice to pasta and toss well to coat. Before serving, adjust consistency with remaining reserved cooking water as needed and season with salt and pepper to taste.