This recipe is from Simply French by Patricia Wells.  I made this for our dinner at Kay Hartman's.  Kay posted this to rec.food.cooking and I've left her comments intact. This was my first experience with Belgian endives, both eating and cooking them, and I liked them a lot.
 
 

Braised Endives
                      Endives "Meuniere"
 

1.  Rinse and dry the endives, and remove any leaves that have darkened.  Trim the ends slightly and using a small knife, remove the bitter cone at the base of each head.  Bring a large pot of water to a boil.  Salt the water, add the lemon juice, 1 tablespoon of the sugar, and the endives, and cook until soft, about 30 minutes.  Drain thoroughly and place in a single layer on a platter.  Sprinkle with 1 tablespoon sugar, salt, and pepper, and set aside until cool enough to handle.  Do not be concerned if the endives brown a bit - they will be browned later in butter.  (The recipe may be prepared to this point several hours in advance.  Cover until needed.)

2.  With your hands, gently but firmly squeeze each endive to extract the bitter liquid.

3.  In a large skillet, melt the butter over moderately high heat.  When hot, add the endives in a single later and brown evenly on each side, about 3 minutes per side.  Remove and drain well.  Transfer the endives to a warmed serving bowl, toss with the remaining 1 tablespoon sugar, and season to taste with salt and pepper.  Serve immediately.  [We left off the last tablespoon of sugar and didn't miss it at all.]

Yield:  4 servings