Step 1

Bring a saucepan of water to a boil. Drop in the onions and boil 2 minutes. Drain and cool slightly.

Step 2

Use a small, sharp knife to slice off the top of the onions, then slip off the skins. Trim any hairy roots, but leave the stem end intact so that the onions don't separate. If the onions are larger than 1 1/2-inches diameter, slice into halves or quarters.

Step 3

Heat the butter and oil in a medium (8-10-inch) nonstick skillet over medium-high heat. When the butter stops foaming and begins to smell nutty, add the onions to the pan. Cook 5 minutes, or until the onions are browned, stirring occasionally.

Step 4

Sprinkle the onions with the sugar and salt. Pour the water and vinegar over them (the pan will sputter). Turn the heat down to medium and cover the pan. Cook 5 minutes.

Step 5

Uncover the pan and continue cooking until the liquid in the pan looks syrupy and has large bubbles, another 2-3 minutes. Sprinkle with the thyme and serve.