Preheat oven to 300 degrees F. Place endives in a stainless steel pot. Add water, sugar, and lemon juice. Cover with a napkin or dishtowel and bring to a boil. Simmer 20 minutes and remove endives. Strain cooking liquid and reserve. Let endives cool and cut into quarters lengthwise. Set aside.
Heat a medium saute pan until very hot and add 2 teaspoons of olive oil. Season scallops with salt and pepper and quickly sear scallops for 3 minutes. Turn the scallops over and cook for 1 minute more. Remove.
In another saute pan, add butter and let brown. Add balsamic vinegar, 2 teaspoons reserved endive cooking liquid, salt, pepper, chopped parsley, tomatoes, and shallots.
On 4 dinner plates, fan out 4 pieces of endive. Warm plates in oven for 2 to 3 minutes. Remove plates from oven and place 3 scallops over endives and lightly nappe with sauce. Serve immediately.