Cut tofu into 4 thin rectangles. Place 4 stacked sheets of paper towel on a cutting board, arrange tofu on top, then cover with 4 more sheets of paper towel and top with a sheet pan and a heavy pot, books, or cans. Allow to drain for about 30 minutes.
When tofu has finished draining heat a large covered pot of salted water over high heat to bring to a boil. Remove tofu from paper towels and place into a ziplock bag or shallow container and pour over buttermilk, toss to coat. Set aside. In a shallow bowl mix together flour, cornstarch, onion powder, 1 tsp salt, and a heavy pinch of black pepper. Set aside.
When water boils add potatoes and cook for 15-20 minutes until very tender.
Meanwhile heat oil in a 12-inch skillet over medium-high heat. When oil shimmers remove tofu from buttermilk, dredge heavily in the flour mixture and then place in the hot oil. Fry for 3-4 minutes per side until nicely browned and crispy. Transfer to a wire rack to cool and sprinkle with salt and cayenne pepper if using.
Drain potatoes and return to pot over low heat. Mash potatoes to desired consistency. Add arugula, butter, and milk and stir to combine. Season with salt and pepper to taste. Add more milk if mashed potatoes are too stiff. Remove from heat.
Serve mashed potatoes topped with fried tofu.