Bring a large pot of water to boil. Add linguine and cook al dente according to package directions. Drain and set aside.

Meanwhile, add broth and cashews to a blender. Blend until smooth, 15 to 20 seconds. Pour through a fine-mesh strainer into a small bowl (discard any solids).

Heat oil in a large high-sided skillet over medium-low heat. Add mushrooms, garlic and rosemary; cook, stirring frequently, until the mushrooms are tender and the garlic is fragrant, 2 to 3 minutes. Add the cashew mixture, milk and soy sauce. Bring to a boil over medium heat; reduce heat to medium-low and simmer, stirring frequently, until the sauce has thickened, 4 to 5 minutes. Add shrimp; simmer, stirring occasionally, until the shrimp is cooked through, 4 to 5 minutes. Add the pasta; cook, stirring constantly, until completely coated in the sauce, about 1 minute. Top with Parmesan and crushed red pepper.