Preheat oven to 350°F. Butter a 1-quart casserole. Melt 1 Tbsp butter and lightly sauté onions until just wilted.
Layer a third of the sliced turnips in the casserole dish; top with a third of the onion; sprinkle with 2 teaspoons of flour, 1/3 teaspoon of salt, and one grind of pepper; pat with dollops from 1 tablespoon of butter. Repeat this, layering twice.
Mix milk and cream together and pour over the turnips. Cover and bake in a 350°F oven for 30 minutes, then remove cover and bake for another 30-45 minutes, or until tender and bubbly.