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1
Trim the beef and cut into about 2-3 inch squares, set on a plastic wrap, cover with the wrap, and pound thin.
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2
Mix together the salt, thyme, black pepper, garlic, cayenne and flour, then toss the meat in it to coat thoroughly.
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3
Heat the oil in a cast iron dutch oven or a similar pan until it is quite hot. Add the meat/seasoned flour (including what is loose in the bowl) and cook until browned on both sides. Remove the meat to a dish.
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4
If there isn't enough oil in the dutch oven to sweat the onions, add a little. Put the onions in and sweat until soft, then add the bell pepper and celery and cook until it is soft. You might need to turn the heat down slightly; you do not want to brown the vegetables, but you want to thoroughly soften them.
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5
Add the tomatoes and stock to the dutch oven and bring to a simmer. Return the meat to the dutch oven and cook at a simmer for 50 minutes to an hour, stirring occasionally, uncovered. Add additional stock if it gets too dry. There will be a moment when the liquid transforms from vegetables and stock to gravy; that, and when the meat is tender, is when it is done.
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6
Meanwhile, when you have about forty minutes to go on the meat and gravy, put the 2 cups of water along with a large pinch of salt in a saucepan and bring to a simmer. Slowly add the grits stirring constantly and bring to a simmer and cook for a half hour, until soft and done. You might need a small amount of additional water.
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7
When the meat is tender and the liquid is gravy-like, taste for salt and pepper. Serve over the cooked grits.