Peel the turnip, then dice into bite size chunks. Place the turnips into a saucepan and fill with water until it barely reaches the top of the turnips. Bring to a boil then cover. Simmer for 5 minutes. Drain the turnips.
Place the turnips into the saucepan again and add water until almost covering the turnips. Add the sugar and combine. Bring to a boil then cover. Simmer until the turnips are fork tender then drain all of the water except for a small amount on the bottom of the pan. Reserve the turnips.
*Note: The reason for boiling the turnips for the second time is to get rid of the bitterness.
Meanwhile, in a separate pan, melt the butter over medium/high heat then add the flour. Stir the mixture constantly to form a paste or roux. Add the milk and continue to stir with a whisk until the mixture thickens. Add the reserved turnips and combine. Add salt and pepper to taste.
You may want to add a little extra milk as you may want a more thin consistency.