Place onions into a large pot and cover with salted water; bring to a boil. Reduce heat to medium-low and simmer until tender, about 10 minutes. Drain.

Melt butter in a large skillet over medium heat; cook and stir flour and nutmeg in melted butter for about 5 minutes; season with salt and pepper. Add cream to flour mixture; cook and stir until bubbly and thick, about 5 minutes more. Stir onion and parsley into cream sauce until heated through, 2 to 3 minutes.