Put the silken tofu and soy sauce in a tall jug and add 3 tablespoons of the reserved pasta water. Use a stick blender to blend to a smooth sauce, then pour into the pan with the mushroom mixture.
Drain the pasta and add it to the pan with the tomato sauce. Turn down to a low heat, add the cream and season with salt and pepper. Add more pasta water if you want the sauce to be looser.
Process until a smooth, creamy sauce forms, 30 to 45 seconds. Return sauce to skillet. Add pasta and reserved cooking liquid to skillet; stir to coat with sauce. Simmer over medium, stirring and ...