Melt 1 tablespoon butter in a large pot over medium-high heat. Add the turnip, potatoes, all but 2 tablespoons of the chopped red onion and a pinch of salt. Cook, stirring occasionally, until the vegetables are slightly softened, about 3 minutes; remove to a plate.
Melt 2 tablespoons butter in the pot. Sprinkle in the flour and curry powder; cook, stirring, 1 minute. Gradually whisk in the broth until smooth. Return the potato mixture to the pot; add the peas and carrots and the sugar. Bring to a boil, then reduce the heat to medium. Cover and simmer 10 minutes; uncover and simmer 5 more minutes. Season with salt and pepper.
Season the steak with salt and pepper. Melt the remaining 1 tablespoon butter in a nonstick skillet over medium-high heat. Add the steak; cook 4 minutes per side. Let rest 5 minutes, then slice against the grain. Serve with the curry and rice. Top with the reserved red onion.