Creamy Gochujang Chicken Noodles

Name: Creamy Gochujang Chicken Noodles
Ingredients: ¼ cup gochujang; 3 Tbsp. vegetable oil, divided; 2 Tbsp. gochugaru chile flakes; 1½ tsp. honey; 1 tsp. paprika; ½ tsp. freshly ground black pepper; ½ tsp. kosher salt; 4 garlic cloves, finely chopped; 4 boneless, skinless chicken thighs, cut into 1-in. pieces; 1 lb. fettuccine; 1½ cups heavy cream; 3 Tbsp. soy sauce; 3 scallions, whites and greens separated, thinly sliced; 8 white mushrooms, thinly sliced; 1 cup grated parmesan (optional)