Place the parsnips in a saucepan with 1/2 teaspoon salt. Cover with cold water and bring to a simmer over medium-high heat. Cook until tender when pierced with a fork, 5 to 7 minutes. Drain and return the pan to the stove.
Add the butter, and once melted, add the peas and sugar. Cook until the peas are heated through, 2 to 3 minutes, and season to taste with salt and pepper. Transfer to a serving dish and serve immediately.