Add potatoes to a large pot and cover with water. Bring to a simmer and cook for 10-15 minutes or until potatoes are fork-tender. Drain and return potatoes to the pot. Add butter and some salt and pepper. Mash with a fork until smooth. Set mashed potatoes aside.

In a small bowl, mix the hot broth with the cornstarch and some salt. Stir until incorporated. Set broth mixture aside.

Heat just half of the oil in a skillet over medium-high heat. Add the tofu and some salt and pepper. Cook, stirring occasionally until crisp, 4-6 minutes. Transfer tofu to a plate.

Heat remaining oil in the same skillet. Add mushrooms and shallot and cook 3-5 until mushrooms begin to brown. Add garlic and cook another minute until fragrant.

Add broth and balsamic vinegar. Bring to a simmer and cook until thickened, about 3-5 minutes.

Return tofu to the skillet and bring to a simmer. Season to taste with some salt and pepper.

Serve tofu marsala with mashed potatoes.