Melt the butter in a large saute pan over medium heat. When the butter is melted, sprinkle in the sugar. Place the endive in the butter-sugar mixture, cut side down. Cook until golden brown, about 5 minutes, lowering the heat if the butter starts to burn. Turn the endives over and brown the other side, about 3 to 5 more minutes. Turn the endive back over and add in the white wine and cook until reduced by half, about 2 minutes. Add the chicken broth, cover and cook until tender and the endives can be easily pierced with a knife, about 15 minutes. If the pan gets too dry, add a tablespoon of water.
Uncover and add the lemon juice and thyme and bring to a simmer for 1 minute. Season, to taste, with salt and pepper. Add the parsley, toss and serve.