Put a large, heavy frying pan, sauté pan, or pot over medium-low heat. (Whatever vessel you choose should have a tight-fitting lid.) When the pan is hot, add the butter.
While the butter melts, trim off and discard any browned bits from the ends of the endives and any bruised or browning exterior leaves.
When the butter is melted, lay the endives in a single layer in the pan.
Sprinkle them with the lemon juice and salt.
Pour the Somerset Ridge Riesling Wine down along the side of the pan (you don't want to wash off the salt you've just sprinkled on).
If you want to cut the bitterness in the final dish even further than the braising will do alone, sprinkle the endives with the sugar.
Cover the pan.
You want a nice, tight fit with the lid. If steam is escaping, lay a piece of foil over the pan and then put on the lid. Or, cut a piece of parchment paper to fit in the pan directly over the endives and then cover the pan (feel free to do this even with a tight-fitting lid; it helps the endives brown evenly).
Reduce the heat to low.
Let the endives cook, undisturbed, until they are very tender, about 30 minutes, or put the pan in a 375F oven (as long as it's oven-safe) and let them cook for 30 to 40 minutes instead of on the stove. (This method is also more likely to result in more evenly browned endives.)
Turn the endives over and cook them until they are browned all over.
(Note that if you added sugar in Step 6, you'll need to watch them quite carefully at this point, since the added sugar will make them brown more quickly.)
Serve them hot or warm.
