Those early French in NOLA, were very thrifty, they'd cook boiled brisket (boulli) for dinner, then use the leftover meat, broth, and vegetables for soup.
From Richard and Rima Colins' The New Orleans Cookbook:
Horseradish Sauce
6 TBS. horseradish
1 TBS. Creole mustard (brown mustard might work if you don't have Creole)
3 TBS. white wine vinegar
1/4 tsp. ground white pepper
1/8 tsp. cayenne
1/8 tsp. sugar
1/2 c. heavy cream
Combine all of the ingredients except for the heavy cream, mix thoroughly, and let stand for 15 minutes, then add the cream. Cover the dish with plastic wrap and refrigerate for at least one hour.
Seasoning for cooking Brisket (recipe call for 2 qts. of water in a stockpot - if you use a crockpot you might be using less water, so you may want to halve some of this.)
(Some of this is me, and some of thisis from the Collins')
2 Beefsteak tomatoes cut in quarters
2 medium onions cut in quarters
6 carrots cut in half, and again crosswise
4 green onions, cut in 3-4" pieces
4 stalks of celery cut up roughly
8-10 stems of parsley
2 TBS. salt
1/1/2 tsp. freshly ground black pepper
2 bay leaves
1 tsp. dried thyme
6 whole cloves
6 whole allspice
1/4 tsp. cayenne
1/4 tsp. mace